New results on free and simple hypermodules
AIMS Mathematics, vol.11, no.6, pp.18202-18221, 2026 (SCI-Expanded, Scopus)
- Publication Type: Article / Article
- Volume: 11 Issue: 6
- Publication Date: 2026
- Doi Number: 10.3934/math.2026740
- Journal Name: AIMS Mathematics
- Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Page Numbers: pp.18202-18221
- Keywords: free hypermodule, simple hypermodule, normal projective (injective) hypermodule
- Open Archive Collection: AVESIS Open Access Collection
- Ataturk University Affiliated: No
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.