The notions of irreducible ideals of the endomorphism ring on the category of rings and the category of modules

https://doi.org/10.24042/ajpm.v13i1.11139

Fitriana Hasnani, Meryta Febrilian Fatimah, Nikken Prima Puspita

Abstract


Let R commutative ring with multiplicative identity, and M is an R-module. An ideal I of R is irreducible if the intersection of every two ideals of R equals I, then one of them is I itself. Module theory is also known as an irreducible submodule, from the concept of an irreducible ideal in the ring. The set of R - module homomorphisms from M to itself is denoted by EndR(M). It is called a module endomorphism M of ring R. The set EndR(M) is also a ring with an addition operation and composition function. This paper showed the sufficient condition of an irreducible ideal on the ring of EndR(R) and EndR(M)


Keywords


Endomorphism; Endomorphism Ring; Irreducible Ideal; Irreducible Submodule

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DOI: https://doi.org/10.24042/ajpm.v13i1.11139

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Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.