Flatness properties of acts over semigroups

IF 0.6 Q3 MATHEMATICS

Categories and General Algebraic Structures with Applications Pub Date : 2021-01-01 DOI:10.52547/cgasa.15.1.59

V. Laan, Ülo Reimaa, L. Tart, Elery Teor

引用次数: 1

Abstract

In this paper we study flatness properties (pullback flatness, limit flatness, finite limit flatness) of acts over semigroups. These are defined by requiring preservation of certain limits from the functor of tensor multiplication by a given act. We give a description of firm pullback flat acts using Conditions (P) and (E). We also study pure epimorphisms and their connections to finitely presented acts and pullback flat acts. We study these flatness properties in the category of all acts, as well as in the category of unitary acts and in the category of firm acts, which arise naturally in the Morita theory of semigroups.

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半群上行为的平坦性

本文研究了半群上行为的平直性(回拉平直性、极限平直性、有限极限平直性)。它们的定义是要求保留给定行为下张量乘法的函子的某些极限。我们利用条件(P)和(E)给出了坚定的回拉平面行为的描述。我们还研究了纯属态及其与有限表示行为和回拉平面行为的联系。我们研究了在半群的Morita理论中自然产生的所有行为范畴、单位行为范畴和坚定行为范畴中的这些平坦性。

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

Categories and General Algebraic Structures with Applications MATHEMATICS-

CiteScore

1.40

自引率

11.10%

发文量

审稿时长

8 weeks

期刊介绍： Categories and General Algebraic Structures with Applications is an international journal published by Shahid Beheshti University, Tehran, Iran, free of page charges. It publishes original high quality research papers and invited research and survey articles mainly in two subjects: Categories (algebraic, topological, and applications in mathematics and computer sciences) and General Algebraic Structures (not necessarily classical algebraic structures, but universal algebras such as algebras in categories, semigroups, their actions, automata, ordered algebraic structures, lattices (of any kind), quasigroups, hyper universal algebras, and their applications.