关于半完全 A 环

Ukrains’kyi Matematychnyi Zhurnal Pub Date : 2024-07-03 DOI:10.3842/umzh.v76i5.7491

Truong Thi Thuy Van, Ahmad M. Alghamdi, Amnah A. Alkinani

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引用次数: 0

摘要

UDC 512.5 如果每个右理想都是自变不变的，那么这个环叫做右 a 环。我们描述了半完全环上 a 环的一些性质。研究表明，一个 I 有限右 a 环是一个半简单阿汀环和一个基本环的直接和。我们还证明，如果 R 是一个不可分解的（作为一个环）I-无限右 a 环，它不简单，具有非琐幂级数，使得每个最小右理想都是一个右湮器，并且 S o c ( R R ) = S o c ( R R ) 在 R R 中是本质的，那么 R 是一个准弗罗贝纽斯环，它也是一个右 q 环。

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On semiperfect a -rings

UDC 512.5 A ring is called a right a -ring if every right ideal is automorphism invariant. We describe some properties of a -rings over semiperfect rings. It is shown that an I-finite right a -ring is a direct sum of a semisimple Artinian ring and a basic ring. It is also demonstrated that if R is an indecomposable (as a ring) I-finite right a -ring not simple with nontrivial idempotents such that every minimal right ideal is a right annihilator and S o c ( R R ) = S o c ( R R ) is essential in R R , then R is a quasi-Frobenius ring and it is also a right q -ring.

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Ukrains’kyi Matematychnyi Zhurnal

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