论左 T 无蕴环

IF 1.1 3区数学 Q1 MATHEMATICS

Results in Mathematics Pub Date : 2024-05-11 DOI:10.1007/s00025-024-02187-3

Ryszard R. Andruszkiewicz, Marek Kȩpczyk

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引用次数: 0

摘要

本文证明了任何由两个左 T-nilpotent 子环组成的环都是左 T-nilpotent 环。论文包含了对所有半群 S 的描述，这样一个 S 阶环 \(R=\bigoplus _{s\in S}A_s\) 具有这样的性质：R 的加法群 \(A_s\)的子群中所有子环的左 T-nilpotency 意味着 R 的左 T-nilpotency 。

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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On Left T-Nilpotent Rings

It is shown that any ring being a sum of two left T-nilpotent subrings is left T-nilpotent. The paper contains the description of all the semigroups S such that an S-graded ring \(R=\bigoplus _{s\in S}A_s\) has the property that the left T-nilpotency of all subrings among the subgroups \(A_s\) of the additive group of R implies the left T-nilpotency of R. Furthermore, this result is extended to rings R being S-sums.

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来源期刊

Results in Mathematics 数学-数学

CiteScore

1.90

自引率

4.50%

发文量

198

审稿时长

6-12 weeks

期刊介绍： Results in Mathematics (RM) publishes mainly research papers in all fields of pure and applied mathematics. In addition, it publishes summaries of any mathematical field and surveys of any mathematical subject provided they are designed to advance some recent mathematical development.