Research article

On centrally-extended -homoderivations on rings

  • In this article, we explored the commutativity of a ring that is equipped with a unique class of mappings called centrally extended -homoderivations, where is an integer. These mappings generalize the concepts of derivations and homoderivations. Furthermore, we investigated specific properties of the center of such rings.

    Citation: M. S. Tammam El-Sayiad, Munerah Almulhem. On centrally-extended -homoderivations on rings[J]. AIMS Mathematics, 2025, 10(3): 7191-7205. doi: 10.3934/math.2025328

    Related Papers:

    [1] Stephen W. Sawyer, Kairui Zhang, Jason A. Horton, Pranav Soman . Perfusion-based co-culture model system for bone tissue engineering. AIMS Bioengineering, 2020, 7(2): 91-105. doi: 10.3934/bioeng.2020009
    [2] Tanishka Taori, Anjali Borle, Shefali Maheshwari, Amit Reche . An insight into the biomaterials used in craniofacial tissue engineering inclusive of regenerative dentistry. AIMS Bioengineering, 2023, 10(2): 153-174. doi: 10.3934/bioeng.2023011
    [3] Maria Júlia Bento Martins Parreira, Bruna Trazzi Pagani, Matheus Bento Medeiros Moscatel, Daniela Vieira Buchaim, Carlos Henrique Bertoni Reis, Beatriz Flávia de Moraes Trazzi, Acácio Fuziy, Rogerio Leone Buchaim . Effects of systemic administration of the retinoid Isotretinoin on bone tissue: A narrative literature review. AIMS Bioengineering, 2024, 11(2): 212-240. doi: 10.3934/bioeng.2024012
    [4] P. Mora-Raimundo, M. Manzano, M. Vallet-Regí . Nanoparticles for the treatment of osteoporosis. AIMS Bioengineering, 2017, 4(2): 259-274. doi: 10.3934/bioeng.2017.2.259
    [5] Chao Hu, Qing-Hua Qin . Bone remodeling and biological effects of mechanical stimulus. AIMS Bioengineering, 2020, 7(1): 12-28. doi: 10.3934/bioeng.2020002
    [6] Fabrizio Belleggia . Hard and soft tissue augmentation of vertical ridge defects with the “hard top double membrane technique”: introduction of a new technique and a case report. AIMS Bioengineering, 2022, 9(1): 26-43. doi: 10.3934/bioeng.2022003
    [7] José Luis Calvo-Guirado, Marta Belén Cabo-Pastor, Francisco Martínez-Martínez, Miguel Ángel Garcés-Villalá, Félix de Carlos-Villafranca, Nuria García-Carrillo, Manuel Fernández-Domínguez . Histologic and histomorphometric evaluation of minicono abutment on implant surrounding tissue healing and bone resorption on implants placed in healed bone. An experimental study in dogs. AIMS Bioengineering, 2023, 10(3): 183-201. doi: 10.3934/bioeng.2023013
    [8] Izgen Karakaya, Nuran Ulusoy . Basics of dentin-pulp tissue engineering. AIMS Bioengineering, 2018, 5(3): 162-178. doi: 10.3934/bioeng.2018.3.162
    [9] Jéssica de Oliveira Rossi, Gabriel Tognon Rossi, Maria Eduarda Côrtes Camargo, Rogerio Leone Buchaim, Daniela Vieira Buchaim . Effects of the association between hydroxyapatite and photobiomodulation on bone regeneration. AIMS Bioengineering, 2023, 10(4): 466-490. doi: 10.3934/bioeng.2023027
    [10] Yihan Zhang . Manufacture of complex heart tissues: technological advancements and future directions. AIMS Bioengineering, 2021, 8(1): 73-92. doi: 10.3934/bioeng.2021008
  • In this article, we explored the commutativity of a ring that is equipped with a unique class of mappings called centrally extended -homoderivations, where is an integer. These mappings generalize the concepts of derivations and homoderivations. Furthermore, we investigated specific properties of the center of such rings.



    The term and concept of “tissue engineering” was officially coined over 30 years ago, in 1988, at a National Science Foundation workshop as “the application of engineering principles and methods from life sciences to a fundamental understanding of the structure-function relationships of normal and pathological mammalian tissues and the development of biological substitutes to restore, maintain or improve tissue function”. While the field of tissue engineering is relatively new, the idea of replacing one tissue by another dates back several centuries [1]. Thus, and for many years now, the replacement by implantation and transplantation of a tissue from a given site to another site in the same patient (an autograft) or in a different patient (a transplant or an allograft) has been innovative and beneficial, but both techniques present major problems. On the one hand, harvesting tissue for an autograft is expensive, painful, limited by anatomical limitations, and associated with donor site morbidity due to infection and injury. On the other hand, allografts and tissue grafts have serious constraints: limit of access to enough tissues or organs for all patients who need it, rejection by the immune system of the recipient patient, potential risks of introduction of infection or disease... [2]. It is in this context that the development of biofabrication strategies arouses considerable interest in order to develop methods, tools and products having the objectives of mimicking and replicating the anatomical and functional characteristics of human tissues.

    Bone tissue is the second largest transplant tissue in the world. Millions of bone grafts (autografts and allografts) are performed each year around the world, while there is currently no satisfactory alternative to bone grafting. Traditional surgical treatments for fractures and bone defects, mainly comprising bone grafts and implantation of metal prostheses, achieve good clinical results, but these treatments also have serious drawbacks, such as infection, pain, cost. high, and the need for additional surgery. In some cases, such as bone defects, osteoporotic fractures, or bone defects/fractures in oncologic patients after radiation therapy, regeneration of bone tissue is hampered, and then requires modern strategies such as bone tissue engineering [3].

    Tissue-engineering technologies involve the intimate interaction between three different components: (1) the scaffolding material that holds and cohesions cells together and forms the physical structure of tissue, i.e. acts as a model for the formation of new tissues, (2) the cells synthesizing the final tissue and (3) the signaling mechanisms (mechanical and/or chemical) that direct cells to express the desired tissue phenotype. Particular attention must be paid to the specific properties of each of these three components, in order to ensure the quality of the modified and neo-synthetized tissue and therefore the potential for clinical success when the engineered tissue is subsequently implanted into an injured site in vivo [4].

    Biological and clinical evaluation of medical devices, including biomaterials, has also been implemented by ISO's ad hoc technical committee since 1988. Since then, sets of standards have been produced and are kept up to date. technological innovation in this highly biomedical field. If it is absorbable, its degradation products must also be biocompatible and not harmful. For application in a living organism, such as humans, all scaffolding materials must have very specific characteristics. First of all, to be defined as a biomaterial, the material must be biocompatible so that it can exist in harmony with the biological fluids, tissues, and cells of the host, without causing harmful effects locally or systemically. In the case of bone tissue, the scaffolding material must exhibit three fundamental bioactivities and properties: osteoinduction, osteoconduction, and osteointegration. Osteoinduction belongs to the ability to induce osteogenic differentiation of a cell that is not yet engaged [5]. In that context, an osteoinductive biomaterial can directly induce osteogenesis through the recruitment, proliferation, and differentiation of bone related stem cells such as mesenchymal stem cells. Osteoconduction refers to the ability to provide the microenvironment allowing the occurrence of in-place bone formation (osteogenesis) and bone growth [6]. Osseointegration refers to the ability of a biomaterial to elaborate direct contacts and anchoring between the exogenic material it-self and the host bone tissue, without growth of fibrous tissue at the bone-implant interface [7]. These 3 fundamental bioactivities and properties can be supported by different physical characteristics related to this specific mineralized hard material, such as stiffness and mechanical strength, viscosity, shear stress, geometry, hydrophilicity, surface charge, wettability, surface roughness and topography, porosity and pore size, permeability, mechanical stability, as well as controlled degradation rate [8]. All these parameters are crucial to encourage cell migration, adhesion, proliferation, and differentiation, but also for nutrients and oxygen transport throughout the scaffolds [9]. Another key consideration for designing a scaffold is its delivery capability through the releasing biological active agents that can induce important properties such as faster healing, antimicrobial, and antitumoral activity.

    Biomaterials can be classified depending on their composition in metals (such as Fe, Mg, Zn and their alloys), ceramics (calcium phosphate ceramics such as hydroxyapatite, biphasic calcium phosphate [BCP] and tricalcium phosphate [TCP], bioactive glasses, zirconia), natural polymers (collagen, silk, chitosan, alginate, elastin, hyaluronic acid and cellulose) or synthetic polymers (such as polylactid acid [PLA], polyglycolic acid [PGA], polylactic co-glycolic acid [PLGA], poly e-caprolactone [PCL], polyethylene glycol [PEG], polybutylene terephthalate [PBT], polyethylene terephthalate [PET], polypropylene fumarate [PPF] or polyacrylic acid [PAA]), composites (defined as made of two or more substrates belonging to the same or different class of materials) and recently nanomaterials including nanoparticles [10]. All these materials can also be functionalized to improve their properties (including the three fundamental properties described above, but also to induce angiogenesis for example) [11].

    The second component for bone tissue engineering belongs to the cell component where several cell types can be used to develop a bone construct, including osteoblast, embryonic stem cells (ESC), mesenchymal stem cells (MSC) and induced pluripotent stem cells (iPSC). All these cell types have largely demonstrated their ability to induce and promote and bone formation, remodeling, and healing [12].

    A finally, the third part of bone tissue engineering is dedicated to signaling mechanisms that can be conveyed by the material itself, depending on its intrinsic properties and characteristics, or provided secondarily exogenously by enriching the final product with growth factors or cytokines (including TGFbeta and BMP, among others), as well as drugs [13].

    At last, the recent advent and democratization of 3D printing processes, allowing the development of complex 3D structures using various biomaterials, opens up new opportunities and great flexibility in the design and production of scaffolds of different structural complexity combining adapted mechanical properties, vascularization and multicellular component [14]. In parallel, computational approaches can be carried out in order to optimize and predict the expected performances of the bone substitute produced by integrated bone tissue engineering. Finally, advances in artificial intelligence (AI), and deep learning in particular, offer the potential to improve both scientific understanding and clinical outcomes in regenerative medicine [15]. With an improved perception of how to integrate artificial intelligence into current research and clinical practice, AI offers an invaluable tool for improving patient outcomes in bone tissue engineering.



    [1] I. N. Herstein, Topics in ring theory, Chicago: University of Chicago Press, 1969.
    [2] H. E. Bell, M. N. Daif, On centrally-extended maps on rings, Beitr. Algebra Geom., 57 (2016), 129–136. https://doi.org/10.1007/s13366-015-0244-8 doi: 10.1007/s13366-015-0244-8
    [3] M. S. Tammam El-Sayiad, N. M. Muthana, Z. S. Alkhamisi, On right generalized -derivations in prime rings, East-West J. Math., 18 (2016), 47–51.
    [4] M. M. El-Soufi, Rings with some kinds of mappings, Cairo University, 2000.
    [5] A. Melaibari, N. Muthana, A. Al-Kenani, Homoderivations on rings, G. Math. Notes, 35 (2016), 1–8.
    [6] E. F. Alharfie, N. M. Mthana, The commutativity of prime rings with homoderivations, Int. J. Adv. Appl. Sci., 5 (2018), 79–81. https://doi.org/10.21833/ijaas.2018.05.010 doi: 10.21833/ijaas.2018.05.010
    [7] E. F. Alharfie, N. M. Mthana, On homoderivations and commutativity of rings, Bull. Int. Math. Virtual. Inst., 9 (2019), 301–304.
    [8] N. Rehman, M. R. Mozumder, A. Abbasi, Homoderivations on ideals of prime and semiprime rings, Aligarh Bull. Math., 38 (2019), 77–87.
    [9] M. S. T. El-Sayiad, M. Almulhem, On centrally extended mappings that are centrally extended additive, AIMS Math., 9 (2024), 33254–33262. https://doi.org/10.3934/math.20241586 doi: 10.3934/math.20241586
    [10] M. M. El-Soufi, A. Ghareeb, Centrally-extended -homoderivations on prime and semiprime rings, J. Math., 2022 (2022), 5. https://doi.org/10.1155/2022/2584177 doi: 10.1155/2022/2584177
    [11] A. Boua, E. Koç Sögütcü, Semiprime rings with generalized homoderivations, Bol. da Soc. Paran. Matematica 41 (2023), 8. https://doi.org/10.5269/bspm.62479 doi: 10.5269/bspm.62479
    [12] M. S. T. El-Sayiad, A. Ageeb, A. Ghareeb, Centralizing -homoderivations of semiprime rings, J. Math., 2022 (2022), 8. https://doi.org/10.1155/2022/1112183 doi: 10.1155/2022/1112183
    [13] L. O. Chung, Nil derivations, J. Algebra, 95 (1985), 20–30. https://doi.org/10.1016/0021-8693(85)90089-4 doi: 10.1016/0021-8693(85)90089-4
    [14] H. E. Bell, M. N. Daif, On commutativity and strong commutativity preserving maps, Canad. Math. Bull., 37 (1994), 443–447. https://doi.org/10.4153/cmb-1994-064-x doi: 10.4153/cmb-1994-064-x
    [15] J. H. Mayne, Centralizing mappings of prime rings, Canad. Math. Bull., 26 (1984), 122–126. https://doi.org/10.4153/cmb-1984-018-2 doi: 10.4153/cmb-1984-018-2
    [16] H. E. Bell, W. S. Martindale, Centralizing mappings of semiprime rings, Can. Math. Bull., 30 (1987), 92–101. https://doi.org/10.4153/CMB-1987-014-x doi: 10.4153/CMB-1987-014-x
    [17] S. Ali, S. Huang, On derivations in semiprime rings, Algebras Rep. Theory, 15 (2012), 1023–1033. https://doi.org/10.1007/s10468-011-9271-9 doi: 10.1007/s10468-011-9271-9
    [18] C. K. Liu, On skew derivations in semiprime rings, Algebras Rep. Theory, 16 (2013), 1561–1576. https://doi.org/10.1007/s10468-012-9370-2 doi: 10.1007/s10468-012-9370-2
    [19] B. L. M. Ferreira, H. Guzzo, R. N. Ferreira, An approach between the multiplicative and additive structure of a Jordan ring, Bull. Iran. Math. Soc., 47 (2021), 961–975. https://doi.org/10.1007/s41980-020-00423-4 doi: 10.1007/s41980-020-00423-4
    [20] J. C. M. Ferreira, B. L. M. Ferreira, Additivity of -multiplicative maps on alternative rings, Comm. Algebra, 44 (2016), 1557–1568. https://doi.org/10.1080/00927872.2015.1027364 doi: 10.1080/00927872.2015.1027364
    [21] B. L. M. Ferreira, H. Julius, D. Smigly, Commuting maps and identities with inverse on alternative division rings, J. Algebra, 638 (2024), 488–505. https://doi.org/10.1016/j.jalgebra.2023.09.022 doi: 10.1016/j.jalgebra.2023.09.022
  • This article has been cited by:

    1. Vincent Deplaigne, Gael Y. Rochefort, Cell–Biomaterial Interactions, 2023, 10, 2306-5354, 241, 10.3390/bioengineering10020241
    2. Katarzyna Klimek, Krzysztof Palka, Wieslaw Truszkiewicz, Timothy E. L. Douglas, Aleksandra Nurzynska, Grazyna Ginalska, Could Curdlan/Whey Protein Isolate/Hydroxyapatite Biomaterials Be Considered as Promising Bone Scaffolds?—Fabrication, Characterization, and Evaluation of Cytocompatibility towards Osteoblast Cells In Vitro, 2022, 11, 2073-4409, 3251, 10.3390/cells11203251
    3. Alexis Delpierre, Guillaume Savard, Matthieu Renaud, Gael Y. Rochefort, Tissue Engineering Strategies Applied in Bone Regeneration and Bone Repair, 2023, 10, 2306-5354, 644, 10.3390/bioengineering10060644
    4. Marco Ruggeri, Barbara Vigani, Silvia Rossi, Giuseppina Sandri, 2025, 9780443220173, 413, 10.1016/B978-0-443-22017-3.00009-3
    5. Weijie Liu, Nalini Cheong, Zhuling He, Tonghan Zhang, Application of Hydroxyapatite Composites in Bone Tissue Engineering: A Review, 2025, 16, 2079-4983, 127, 10.3390/jfb16040127
  • Reader Comments
  • © 2025 the Author(s), licensee AIMS Press. This is an open access article distributed under the terms of the Creative Commons Attribution License (http://creativecommons.org/licenses/by/4.0)
通讯作者: 陈斌, bchen63@163.com
  • 1. 

    沈阳化工大学材料科学与工程学院 沈阳 110142

  1. 本站搜索
  2. 百度学术搜索
  3. 万方数据库搜索
  4. CNKI搜索

Metrics

Article views(209) PDF downloads(18) Cited by(0)

Article outline

Other Articles By Authors

/

DownLoad:  Full-Size Img  PowerPoint
Return
Return

Catalog