New results on free and simple hypermodules

Ergül Türkmen; Fatma Kahriman; Yıldız Aydın; Ergül Türkmen; Fatma Kahriman; Yıldız Aydın

doi:10.3934/math.2026740

AIMS Mathematics

2026, Volume 11, Issue 6: 18202-18221. doi: 10.3934/math.2026740

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New results on free and simple hypermodules

1.
Amasya University, Faculty of Art and Science, Department of Mathematics, Amasya, Turkey
2.
Atatürk University, Faculty of Science, Department of Mathematics, Erzurum, Turkey
3.
Amasya University, Institute of Science and Technology, Amasya, Turkey
4.
Istanbul Gelişim University, Department of Management and Information Systems, İstanbul, Turkey

Received: 07 May 2026 Revised: 08 June 2026 Accepted: 15 June 2026 Published: 22 June 2026
MSC : 16Y20, 18A99

In this paper, we investigate the relationship between free hypermodules and normal projective hypermodules. In particular, we prove that every cyclic free $ R $-hypermodule is normal projective and establish a criterion characterizing the normal projectivity of subhypermodules of the free hypermodule $ H(R) $, where $ R $ is a hyperring. In addition, by means of quotient hypermodule constructions, we provide an example of a free hypermodule arising from a free module. Furthermore, we study the normal injectivity of simple hypermodules and obtain a fundamental characterization of hyperrings whose simple hypermodules are normal injective.
- free hypermodule,
- simple hypermodule,
- normal projective (injective) hypermodule
Citation: Ergül Türkmen, Fatma Kahriman, Yıldız Aydın. New results on free and simple hypermodules[J]. AIMS Mathematics, 2026, 11(6): 18202-18221. doi: 10.3934/math.2026740

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Abstract

In this paper, we investigate the relationship between free hypermodules and normal projective hypermodules. In particular, we prove that every cyclic free $ R $-hypermodule is normal projective and establish a criterion characterizing the normal projectivity of subhypermodules of the free hypermodule $ H(R) $, where $ R $ is a hyperring. In addition, by means of quotient hypermodule constructions, we provide an example of a free hypermodule arising from a free module. Furthermore, we study the normal injectivity of simple hypermodules and obtain a fundamental characterization of hyperrings whose simple hypermodules are normal injective.

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