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

Fitriana Hasnani, Meryta Febrilian Fatimah, N. P. Puspita
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引用次数: 1

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)
环范畴和模范畴上自同态环不可约理想的概念
设R为可交换环,具有乘法恒等式,M是一个R模。R的理想I是不可约的如果R的每两个理想的交集等于I,那么其中一个就是I本身。模理论也被称为不可约子模,来自环中不可约理想的概念。M到自身的R -模同态集合用EndR(M)表示。称为环r的模自同态M。集合EndR(M)也是一个具有加法运算和复合函数的环。本文给出了EndR(R)和EndR(M)环上不可约理想的充分条件。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
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