A hyperstructural approach to essentiality. Issue 11 (2nd November 2018)

• Record Type: Journal Article
• Authors: Hamzekolaee, Ali Reza Moniri; Norouzi, Morteza
• Is Part Of: Communications in algebra. Volume 46:Issue 11(2018)
• Page Start: 4954
• Page End: 4964
• Publication Date: 2018-11-02
• Subjects: Direct summand -- extending hypermodule -- essential subhypermodule; 20N20 -- 16D10 -- 16D50; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1459649
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let M be a hypermodule over a hyperring R such that the intersection of any two subhypermodules of M, is a subhypermodule of M . We introduce the concept of an essential subhypermodule in M relative to an arbitrary subhypermodule T of M, which is called a T -essential subhypermodule of M . Our main goal in this work is to investigate properties of (relative) essential subhypermodules. We apply this concept to introduce extending hypermodules. Examples are provided to illustrate different concepts.