2-Products of Idempotent by Nilpotent Matrices

IF 0.7 4区数学 Q2 MATHEMATICS Bulletin of The Iranian Mathematical Society Pub Date : 2024-07-31 DOI:10.1007/s41980-024-00883-y

Grigore Călugăreanu, Horia F. Pop

引用次数: 0

Abstract

Over Prüfer domains, we characterize idempotent by nilpotent 2-products of $2\times 2$ matrices. Nilpotents are always such products. We also provide large classes of rings over which every $2\times 2$ idempotent matrix is such a product. Finally, for $2\times 2$ matrices over GCD domains, idempotent–nilpotent products which are also nilpotent–idempotent products are characterized.

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2-无效矩阵的等价积

在Prüfer域上，我们通过矩阵（2\times 2\) 的零potent 2-products来描述idempotent。零potent 总是这样的乘积。我们还提供了大类的环，在这些环上，每个（2次2）幂等矩阵都是这样的乘积。最后，对于 GCD 域上的$2\times 2$ 矩阵，我们描述了偶能-零potent 乘积也是零potent-偶能乘积的特征。

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

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0.00%

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期刊介绍： The Bulletin of the Iranian Mathematical Society (BIMS) publishes original research papers as well as survey articles on a variety of hot topics from distinguished mathematicians. Research papers presented comprise of innovative contributions while expository survey articles feature important results that appeal to a broad audience. Articles are expected to address active research topics and are required to cite existing (including recent) relevant literature appropriately. Papers are critically reviewed on the basis of quality in its exposition, brevity, potential applications, motivation, value and originality of the results. The BIMS takes a high standard policy against any type plagiarism. The editorial board is devoted to solicit expert referees for a fast and unbiased review process.

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