Driss Bennis, Rachid El Maaouy, J. R. García Rozas, Luis Oyonarte
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引用次数: 0
Abstract
We introduce the concepts of relative (strongly) cotorsion and relative Gorenstein cotorsion modules for a non-necessarily semidualizing module and prove that there exists a unique hereditary abelian model structure where the cofibrations are the monomorphisms with relative Gorenstein flat cokernel and the fibrations are the epimorphisms with relative cotorsion kernel belonging to the Bass class. In the particular case of a semidualizing module, we investigate the existence of abelian model structures on the category of left (right) R-modules where the cofibrations are the epimorphisms (monomorphisms) with kernel (cokernel) belonging to the Bass (Auslander) class. We also show that the class of relative Gorenstein flat modules and the Bass class are part of weak AB-contexts.
我们为一个非必然半化模块引入了相对（强）扭转模块和相对戈伦斯坦扭转模块的概念，并证明存在一个唯一的遗传无性模型结构，其中共纤是具有相对戈伦斯坦平面内核的单形变，纤是具有相对扭转内核的属于巴斯类的外形变。在半双化模子的特殊情况下，我们研究了左（右）R 模子范畴中的无边模型结构的存在性，其中共纤是具有属于 Bass（Auslander）类的核（cokernel）的外变形（单变形）。我们还证明了相对戈伦斯坦平面模块类和巴斯类是弱 AB 上下文的一部分。
期刊介绍：
The Journal of Algebra and Its Applications will publish papers both on theoretical and on applied aspects of Algebra. There is special interest in papers that point out innovative links between areas of Algebra and fields of application. As the field of Algebra continues to experience tremendous growth and diversification, we intend to provide the mathematical community with a central source for information on both the theoretical and the applied aspects of the discipline. While the journal will be primarily devoted to the publication of original research, extraordinary expository articles that encourage communication between algebraists and experts on areas of application as well as those presenting the state of the art on a given algebraic sub-discipline will be considered.
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