Primary decompositions of unital locally matrix algebras

IF 16.4 1区化学 Q1 CHEMISTRY, MULTIDISCIPLINARY

Accounts of Chemical Research Pub Date : 2019-11-25 DOI:10.1142/s166436072050006x

O. Bezushchak, B. Oliynyk

引用次数: 12

Abstract

We construct a unital locally matrix algebra of uncountable dimension that (1) does not admit a primary decomposition, (2) has an infinite locally finite Steinitz number. It gives negative answers to questions from [V. M. Kurochkin, On the theory of locally simple and locally normal algebras, Mat. Sb., Nov. Ser. 22(64)(3) (1948) 443–454; O. Bezushchak and B. Oliynyk, Unital locally matrix algebras and Steinitz numbers, J. Algebra Appl. (2020), online ready]. We also show that for an arbitrary infinite Steinitz number [Formula: see text] there exists a unital locally matrix algebra [Formula: see text] having the Steinitz number [Formula: see text] and not isomorphic to a tensor product of finite-dimensional matrix algebras.

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一元局部矩阵代数的初等分解

构造了一个维数不可数的一元局部矩阵代数，其(1)不允许初等分解，(2)具有无限的局部有限Steinitz数。它对[V.]的问题给出了否定的答案。M. Kurochkin，关于局部简单代数和局部正规代数的理论，vol . b. vol . 22(64)(3) (1948) 443-454;刘建军，单元局部矩阵代数与Steinitz数，代数学报。(2020)，在线准备]。我们还证明了对于任意无限Steinitz数[公式:见文]，存在具有Steinitz数[公式:见文]且与有限维矩阵代数的张量积不同构的一元局部矩阵代数[公式:见文]。

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

Accounts of Chemical Research 化学-化学综合

CiteScore

31.40

自引率

1.10%

发文量

312

审稿时长

2 months

期刊介绍： Accounts of Chemical Research presents short, concise and critical articles offering easy-to-read overviews of basic research and applications in all areas of chemistry and biochemistry. These short reviews focus on research from the author’s own laboratory and are designed to teach the reader about a research project. In addition, Accounts of Chemical Research publishes commentaries that give an informed opinion on a current research problem. Special Issues online are devoted to a single topic of unusual activity and significance. Accounts of Chemical Research replaces the traditional article abstract with an article "Conspectus." These entries synopsize the research affording the reader a closer look at the content and significance of an article. Through this provision of a more detailed description of the article contents, the Conspectus enhances the article's discoverability by search engines and the exposure for the research.