Generalized Stability of the Class of Injective S-Acts

IF 0.4 3区数学 Q4 LOGIC

Algebra and Logic Pub Date : 2023-11-01 DOI:10.1007/s10469-023-09718-x

A. A. Stepanova

引用次数: 0

Abstract

The concept of P-stability is a particular case of generalized stability of complete theories. We study injective S-acts with a P-stable theory. It is proved that the class of injective S-acts is (P, 1)-stable only if S is a one-element monoid. Also we describe commutative and linearly ordered monoids S the class of injective S-acts over which is (P, s)-, (P, a)-, and (P, e)-stable.

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注入式 S-行为类的广义稳定性

P-stability 概念是完整理论广义稳定性的一种特殊情况。我们研究具有 P 稳定性理论的注入式 S 行为。研究证明，只有当 S 是单元素单元时，注入式 S 作用类才是（P，1）稳定的。此外，我们还描述了交换和线性有序单元 S，其上的注入式 S-行为类是（P，s）-、（P，a）-和（P，e）-稳定的。

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

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.