Projections of Finite Rings

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2024-08-16 DOI:10.1007/s10469-024-09750-5

S. S. Korobkov

引用次数: 0

Abstract

Let R and R^φ be associative rings with isomorphic subring lattices, and φ be a lattice isomorphism (or else a projection) of the ring R onto the ring R^φ. We call R^φ the projective image of a ring R and call R itself the projective preimage of a ring R^φ. The main result of the first part of the paper is Theorem 5, which proves that the projective image R^φ of a one-generated finite p-ring R is also one-generated if R^φ at the same time is itself a p-ring. In the second part, we continue studying projections of matrix rings. The main result of this part is Theorems 6 and 7, which prove that if R = M_n(K) is the ring of all square matrices of order n over a finite ring K with identity, and φ is a projection of the ring R onto the ring R^φ, then R^φ = M_n(K′), where K′ is a ring with identity, lattice-isomorphic to the ring K.

查看原文本刊更多论文

有限环的投影

设 R 和 Rφ 是具有同构子环晶格的关联环，φ 是环 R 到环 Rφ 的晶格同构（或投影）。我们称 Rφ 为环 R 的投影像，称 R 本身为环 Rφ 的投影前像。本文第一部分的主要结果是定理 5，它证明了如果 Rφ 同时本身是一个 p 环，那么单生成有限 p 环 R 的投影图 Rφ 也是单生成的。在第二部分，我们继续研究矩阵环的投影。这部分的主要结果是定理 6 和 7，它们证明了如果 R = Mn(K)是有限环 K 上所有 n 阶方阵的同位环，并且 φ 是环 R 在环 Rφ 上的投影，那么 Rφ = Mn(K′)，其中 K′是与环 K 格点同构的同位环。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

求助全文

约1分钟内获得全文求助全文

来源期刊

Algebra and Logic 数学-数学

CiteScore

1.10

自引率

20.00%

发文量

审稿时长

>12 weeks

期刊介绍： This bimonthly journal publishes results of the latest research in the areas of modern general algebra and of logic considered primarily from an algebraic viewpoint. The algebraic papers, constituting the major part of the contents, are concerned with studies in such fields as ordered, almost torsion-free, nilpotent, and metabelian groups; isomorphism rings; Lie algebras; Frattini subgroups; and clusters of algebras. In the area of logic, the periodical covers such topics as hierarchical sets, logical automata, and recursive functions. Algebra and Logic is a translation of ALGEBRA I LOGIKA, a publication of the Siberian Fund for Algebra and Logic and the Institute of Mathematics of the Siberian Branch of the Russian Academy of Sciences. All articles are peer-reviewed.