逼近的二元化、（aleph _1）投影性和沃培卡原理

IF 0.6 4区数学 Q3 MATHEMATICS

Applied Categorical Structures Pub Date : 2024-11-02 DOI:10.1007/s10485-024-09791-y

Asmae Ben Yassine, Jan Trlifaj

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引用次数: 0

摘要

通过萨尔斯对偶性，模块的近似类作为反转对的成分出现。在此，我们考虑模块的一般近似类，并根据这些类的闭合性质研究对偶的可能性。虽然有些证明很容易对偶化，但其他对偶化需要大的心性原则，而且有些证明在 ZFC 中是失败的，非完备环上的\(\aleph _1\)-投影模块类提供了反例。例如，我们证明了 "在同态映像下封闭的模块的每个覆盖类对于模块 M 是 \({\mathrm{Gen\,}}(M)\) 形式 "等价于沃佩卡原理。

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Dualizations of Approximations, \(\aleph _1\)-Projectivity, and Vopěnka’s Principles

The approximation classes of modules that arise as components of cotorsion pairs are tied up by Salce’s duality. Here we consider general approximation classes of modules and investigate possibilities of dualization in dependence on closure properties of these classes. While some proofs are easily dualized, other dualizations require large cardinal principles, and some fail in ZFC, with counterexamples provided by classes of \(\aleph _1\)-projective modules over non-perfect rings. For example, we show that the statement “each covering class of modules closed under homomorphic images is of the form \({\mathrm{Gen\,}}(M)\) for a module M” is equivalent to Vopěnka’s Principle.

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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.