Semirings generated by idempotents

IF 0.5 3区数学 Q3 MATHEMATICS

Journal of Algebra and Its Applications Pub Date : 2024-05-25 DOI:10.1142/s0219498825502846

David Dolžan

引用次数: 0

Abstract

We prove that a semiring multiplicatively generated by its idempotents is commutative and Boolean, if every idempotent in the semiring has an orthogonal complement. We prove that a semiring additively generated by its idempotents is commutative, if every idempotent in the semiring has an orthogonal complement and all the nilpotents in the semirings are central. We also provide examples that the assumptions on the existence of orthogonal complements of idempotents and the centrality of nilpotents cannot be omitted.

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幂等子生成的半环

我们证明，如果由等幂项乘法生成的配线中的每个等幂项都有一个正交补码，那么这个配线就是交换型布尔配线。我们将证明，如果幂级数中的每个幂级数都有一个正交补码，并且幂级数中的所有零点都是中心点，那么由其幂级数加法生成的谓词就是交换谓词。我们还举例说明了不能省略幂级数的正交补码和零点的中心性这两个假设。

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

Journal of Algebra and Its Applications 数学-数学

CiteScore

1.50

自引率

12.50%

发文量

226

审稿时长

4-8 weeks

期刊介绍： The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.