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AIMS Mathematics

2020, Volume 5, Issue 6: 7350-7358. doi: 10.3934/math.2020470
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Research article

Locally finiteness and convolution products in groupoids

  • 1.
    Department of Mathematics, Incheon National University, Incheon, 22012, Korea
  • 2.
    Research Institute of Natural Sciences, Department of Mathematics, Hanyang University, Seoul, 04763, Korea
  • 3.
    Department of Mathematics, University of Alabama, Tuscaloosa, AL, 35487-0350, USA
  • Published: 18 September 2020

  • MSC : 20N02, 06A06, 11M06

  • In this paper, we introduce a version of the Moebius function and other special functions on a particular class of intervals for groupoids, and study them to obtain results analogous to those obtained in the usual lattice, combinatorics and number theory setting, but of course much more general due to the viewpoint taken in this paper.

    Citation: In Ho Hwang, Hee Sik Kim, Joseph Neggers. Locally finiteness and convolution products in groupoids[J]. AIMS Mathematics, 2020, 5(6): 7350-7358. doi: 10.3934/math.2020470

    Related Papers:

  • In this paper, we introduce a version of the Moebius function and other special functions on a particular class of intervals for groupoids, and study them to obtain results analogous to those obtained in the usual lattice, combinatorics and number theory setting, but of course much more general due to the viewpoint taken in this paper.


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    [1] R. H. Bruck, A Survey of Binary Systems, Springer: New York, 1971.
    [2] O. Borůvka, Foundations of the Theory of Groupoids and Groups, John Wiley & Sons: New York, NY, USA, 1976.
    [3] L. Nebeský, Travel groupoids, Czech. Math. J., 56 (2006), 659-675.
    [4] P. J. Allen, H. S. Kim, J. Neggers, Several types of groupoids induced by two-variables functions, Springer Plus, 5 (2016), 1715-1725.
    [5] Y. H. Kim, H. S. Kim, J. Neggers, Selective groupoids and frameworks induced by fuzzy subsets, Iran. J. Fuzzy Syst., 14 (2017), 151-160.
    [6] Y. L. Liu, H. S. Kim, J. Neggers, Hyperfuzzy subsets and subgroupoids, J. Intell. Fuzzy Syst., 33 (2017), 1553-1562.
    [7] I. H. Hwang, H. S. Kim, J. Neggers, Some implicativies for groupoids and BCK-algebras, Mathematics, 7 (2019), 973.
    [8] H. S. Kim, J. Neggers, K. S. So, Order related concepts for arbitrary groupoids, B. Korean Math. Soc., 54 (2017), 1373-1386.
    [9] C. Berge, Principles of Combinatorics, Academic Press, New York, 1971.
    [10] R. P. Stanley, Enumerative Combinatorics, Volume 1, Wadsworth & Brooks/Cole, Monterey, 1986.
    [11] J. Neggers, H. S. Kim, Basic Posets, World Scientific Publishing Com., Singapore, 1998.
    [12] J. M. Howie, An introduction to semigroup theory, Academic Press, New York, 1976.
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  • © 2020 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)
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