带局部单元的环的莫里塔等价性和莫里塔对偶性以及投影单元模子子类

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-04-05 DOI:10.1007/s10485-024-09764-1

Ziba Fazelpour, Alireza Nasr-Isfahani

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引用次数: 0

摘要

我们研究具有局部单元的环的莫里塔等价性和莫里塔对偶性。我们将奥斯兰德关于莫里塔等价性理论和阿祖马亚-莫里塔对偶定理的结果扩展到有局部单元的环。因此，我们用有限生成的投影单元模块的全子类和有限生成的注入单元模块的全子类给出了有局部单元的环上的莫里塔定理和阿祖马亚-莫里塔对偶定理的版本。

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Morita Equivalence and Morita Duality for Rings with Local Units and the Subcategory of Projective Unitary Modules

We study Morita equivalence and Morita duality for rings with local units. We extend Auslander’s results on the theory of Morita equivalence and the Azumaya–Morita duality theorem to rings with local units. As a consequence, we give a version of Morita theorem and Azumaya–Morita duality theorem over rings with local units in terms of their full subcategory of finitely generated projective unitary modules and full subcategory of finitely generated injective unitary modules.

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来源期刊

Applied Categorical Structures 数学-数学

CiteScore

1.30

自引率

16.70%

发文量

审稿时长

>12 weeks

期刊介绍： Applied Categorical Structures focuses on applications of results, techniques and ideas from category theory to mathematics, physics and computer science. These include the study of topological and algebraic categories, representation theory, algebraic geometry, homological and homotopical algebra, derived and triangulated categories, categorification of (geometric) invariants, categorical investigations in mathematical physics, higher category theory and applications, categorical investigations in functional analysis, in continuous order theory and in theoretical computer science. In addition, the journal also follows the development of emerging fields in which the application of categorical methods proves to be relevant. Applied Categorical Structures publishes both carefully refereed research papers and survey papers. It promotes communication and increases the dissemination of new results and ideas among mathematicians and computer scientists who use categorical methods in their research.