Finite rings in varieties with definable principal congruences

Author:

Simons G. E.

Abstract

A variety V \mathcal {V} of rings has definable principal congruences if there is a first-order formula defining principal two-sided ideals for all rings in V \mathcal {V} . Any variety of commutative rings has definable principal congruences, but many non-commutative rings cannot be in a variety with definable principal congruences. We show that a finite ring in a variety with definable principal congruences is a direct product of finite local rings. This result is used to describe the structure of all finite rings R with J ( R ) 2 = 0 J{(R)^2} = 0 in a variety with definable principal congruences.

Publisher

American Mathematical Society (AMS)

Subject

Applied Mathematics,General Mathematics

Reference17 articles.

1. Graduate Texts in Mathematics;Anderson, Frank W.,1992

2. Definable normal closures in locally finite varieties of groups;Baker, Kirby A.;Houston J. Math.,1981

3. The number of subdirectly irreducible algebras in a variety;Baldwin, John T.;Algebra Universalis,1975

4. Definable principal congruences in varieties of groups and rings;Burris, Stanley;Algebra Universalis,1979

5. A correction to: “Definable principal congruences in varieties of groups and rings” [Algebra Universalis 9 (1979), no. 2, 152–164; MR 80c:08004];Burris, S.;Algebra Universalis,1981

Cited by 2 articles. 订阅此论文施引文献 订阅此论文施引文献,注册后可以免费订阅5篇论文的施引文献,订阅后可以查看论文全部施引文献

1. Definable principal congruences and solvability;Annals of Pure and Applied Logic;2009-01

2. FINITE RINGS WITH COMMUTING NILPOTENT ELEMENTS;Communications in Algebra;1996-01

同舟云学术

1.学者识别学者识别

2.学术分析学术分析

3.人才评估人才评估

"同舟云学术"是以全球学者为主线,采集、加工和组织学术论文而形成的新型学术文献查询和分析系统,可以对全球学者进行文献检索和人才价值评估。用户可以通过关注某些学科领域的顶尖人物而持续追踪该领域的学科进展和研究前沿。经过近期的数据扩容,当前同舟云学术共收录了国内外主流学术期刊6万余种,收集的期刊论文及会议论文总量共计约1.5亿篇,并以每天添加12000余篇中外论文的速度递增。我们也可以为用户提供个性化、定制化的学者数据。欢迎来电咨询!咨询电话:010-8811{复制后删除}0370

www.globalauthorid.com

TOP

Copyright © 2019-2024 北京同舟云网络信息技术有限公司
京公网安备11010802033243号  京ICP备18003416号-3