具有半净镍性能的合金环

Vijay. Venkatachalam, Selvaraj Chelliah
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引用次数: 2

摘要

如果环R中的一个元素是R中的幂零元素和周期元素的和,则称它是半零干净的。如果环R中的一个元素是R中的单位元素和周期元素的和,则称它是半零干净的。如果R中的每个元素都是半nil-clean(如:semiclean)。讨论了半零净环的一些基本性质,并研究了半零净环和半净环在各种交换环环境下的性质,如合并和环R的多项式R[x]环。
本文章由计算机程序翻译,如有差异,请以英文原文为准。
Amalgamated rings with semi nil-clean properties
An element in a ring R is said to be semi nil-clean if it is a sum of nilpotent and periodic elements in R. An element in a ring R is said to be semiclean if it is a sum of unit and periodic elements in R. A ring R is said to be semi nil-clean (resp., semiclean) if every element in R is semi nil-clean (resp., semiclean). We discuss some basic properties of semi nil-clean ring and we also study the concepts of semi nil-clean and semiclean properties in various context of commutative rings such as amalgamations and the ring of polynomials R[x] of a ring R.
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