Morita contexts and unitary ideals of rings

IF 1 4区综合性期刊 Q3 MULTIDISCIPLINARY SCIENCES

Proceedings of the Estonian Academy of Sciences Pub Date : 2021-01-01 DOI:10.3176/PROC.2021.2.02

V. Laan, K. Väljako

引用次数: 2

Abstract

In this paper we study Morita contexts between rings without identity. We prove that if two associative rings are connected by a Morita context with surjective mappings, then these rings have isomorphic quantales of unitary ideals. We also show that the quotient rings by ideals that correspond to each other under that isomorphism are connected by a Morita context with surjective mappings. In addition, we consider how annihilators and two-sided socles behave under that isomorphism.

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森田语境与环的酉理想

本文研究了无恒等环间的森田语境。证明了如果两个结合环由一个满射映射的Morita上下文连接，则这两个环具有幺正理想的同构量子。我们还证明了在该同构下彼此对应的理想商环是由具有满射映射的Morita上下文连接起来的。此外，我们还考虑了湮灭子和双面球在这种同构下的行为。

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

Proceedings of the Estonian Academy of Sciences 综合性期刊-综合性期刊

CiteScore

1.80

自引率

22.20%

发文量

审稿时长

>12 weeks

期刊介绍： The Proceedings of the Estonian Academy of Sciences is an international scientific open access journal published by the Estonian Academy of Sciences in collaboration with the University of Tartu, Tallinn University of Technology, Tallinn University, and the Estonian University of Life Sciences. The journal publishes primary research and review papers in the English language. All articles are provided with short Estonian summaries. All papers to be published in the journal are peer reviewed internationally. The journal is open to word-wide scientific community for publications in all fields of science represented at the Estonian Academy of Sciences and having certain connection with our part of the world, North Europe and the Baltic area in particular.