@article{Türkmen2026, 
author = {Ergül Türkmen and Fatma Kahriman and Yıldız Aydın},
title = {New results on free and simple hypermodules},
year = {2026},
journal = {AIMS Mathematics},
volume = {11},
number = {6},
pages = {18202-18221},
keywords = {free hypermodule, simple hypermodule, normal projective (injective) hypermodule},
url = {https://www.sciopen.com/article/10.3934/math.2026740},
doi = {10.3934/math.2026740},
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.}
}