$$\mathfrak {cP}$$ -Baer Polynomial Extensions

IF 0.7 4区数学 Q2 MATHEMATICS

Bulletin of The Iranian Mathematical Society Pub Date : 2024-07-01 DOI:10.1007/s41980-024-00898-5

Nasibeh Aramideh, Ahmad Moussavi

引用次数: 0

Abstract

A ring R is called right $\mathfrak {cP}$-Baer if the right annihilator of a cyclic projective right R-module in R is generated by an idempotent. These rings are a generalization of the right p.q.-Baer rings and abelian rings. Following Birkenmeier and Heider (Commun Algebra 47(3):1348–1375, 2019 https://doi.org/10.1080/00927872.2018.1506462), we investigate the transfer of the $\mathfrak {cP}$-Baer property between a ring R and many polynomial extensions (including skew polynomials, skew Laurent polynomials, skew power series, skew inverse Laurent series), and monoid rings. As a consequence, we answer a question posed by Birkenmeier and Heider (2019).

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$$mathfrak {cP}$$ -Baer 多项式扩展

如果 R 中循环投影右 R 模块的右湮子是由一个幂等子生成的，那么这个环 R 就叫做右 $\mathfrak {cP}$-Baer 环。这些环是右 p.q.-Baer 环和无常环的一般化。继 Birkenmeier 和 Heider (Commun Algebra 47(3):1348-1375, 2019 https://doi.org/10.1080/00927872.2018.1506462)之后，我们研究了环 R 和许多多项式扩展（包括偏斜多项式、偏斜劳伦特多项式、偏斜幂级数、偏斜逆劳伦特数列）以及单元环之间的 $\mathfrak {cP}$-Baer 性质的转移。因此，我们回答了 Birkenmeier 和 Heider（2019）提出的一个问题。

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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来源期刊

Bulletin of The Iranian Mathematical Society Mathematics-General Mathematics

CiteScore

1.40

自引率

0.00%

发文量

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