一、报告题目：The subcategories of exact modules and RSS-equivalences

二、报告人：扶先辉 教授

三、报告时间：2026年5月24号（周日）10:30—11:30

四、报告地点：A4-305

报告摘要：Let R be an Artin algebra, M an R-R bimodule, and Λ = R n M the trivial extension of R by M . The ⊗-exact Λ-module is defined to be the module (X, f ) such that X⊗M⊗M −→X⊗M−→ X is exact, whereas, the Hom-exact Λ-module is defined dually, that is, it is the module (X, f ) such that X −→ Hom(M, X) −→ Hom(M, HomR(M, X)) is exact. Denoted by S(R, M ) the subcategory of ⊗-exact Λ-modules, and by F(M, R) the subcategory of Hom-exact Λ-modules. It is shown S(R, M ) is a resolving subcategory of mod-Λif and only if M is a projective module.

If M and Hom(M, R) are projective modules, then it is proved that F(R, M ) is a Frobenius exact category if and only if R is self-injective. Moreover, when M⊗M = 0, it is shown that there is a unique cotilting right Λ-module T(DR), up to the multiplicity of the indecomposable direct summands, such that S(R, M ) =^⊥T(DR) and, that S(M, R) has Auslander-Reiten sequences. Finally, if M is an exchangeable bimodule, we establish the Ringel-Schmidmeier-Simson equivalence between S(M, R) and F(M, R) under the condition M ⊗R M = 0. These generalize results given by

Xiong-Zhang-Zhang , and Gao-Ma-Liu in [1]. This is an ongoing work with Lifang Qin.

报告人简介：扶先辉，东北师范大学数学与统计学院副院长，教授，博士生导师。研究领域为同调代数和K-理论，现致力于逼近理论及其相关课题的研究，研究工作发表于Adv.Math.， Proc. London Math. Soc.，J. Algebra，J.Pure Appl. Algebra等权威数学杂志。多次主持国家自然科学基金项目，并曾在第十三届全国代数学学术会议和第八届中日韩国际环论会议做大会报告。

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