正则环子半群的最大半格分解

IF 0.8 2区数学 Q2 MATHEMATICS

Journal of Algebra Pub Date : 2025-07-17 DOI:10.1016/j.jalgebra.2025.06.043

Xavier Mary

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引用次数: 0

摘要

结合半群论、环论和格论的论证，在Hannah和O'Meara[25]对正则分离环的幂等子半群的研究基础上，完整地刻画了正则环的某些子半群的最大半格分解。特别地，我们证明了单位正则环的最大同态像是由环的主理想的加性半格给出的。给出了许多例子。

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On the greatest semilattice decomposition of subsemigroups of regular rings

Combining arguments issued from semigroup theory, ring theory and lattice theory, we build up on a study of the idempotent-generated subsemigroup of regular separative rings by Hannah and O'Meara [25] to completely characterize the greatest semilattice decomposition of certain subsemigroups of regular rings. In particular, we prove that the greatest homomorphic image of a unit-regular ring is given by the additive semilattice of principal ideals of the ring. Many examples are given.

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来源期刊

Journal of Algebra 数学-数学

CiteScore

1.50

自引率

22.20%

发文量

414

审稿时长

2-4 weeks

期刊介绍： The Journal of Algebra is a leading international journal and publishes papers that demonstrate high quality research results in algebra and related computational aspects. Only the very best and most interesting papers are to be considered for publication in the journal. With this in mind, it is important that the contribution offer a substantial result that will have a lasting effect upon the field. The journal also seeks work that presents innovative techniques that offer promising results for future research.