张量环上的Ding内射模

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中图分类号：0154.2 文献标识码：A 文章编号：1674-0033(2025)06-0026-05

Ding Injective Modules over Tensor Rings

ZHOU Xing-chi

(College of Mathematical Science,Chongqing Normal University,Shapingba 4O1331, Chongqing)

Abstract: To study the homological properties of Ding injective modules over tensor rings,let R be any ring, M be a finitely generated nilpotent R -bimodule, is the tensor ring.The corepresentation category Cor(HomR(M,-)) of the functor HomR(M,-) is introduced,and the homological properties of Ding injective modules over tensor rings are given by using the full subcategory Depi(HomR(M,-)) ,under certain conditions, if M is a Ding compatible module,then the Ding injective module category over the tensor ring isegea Depi(HomR(M,-)) ：

Key words: tensor ring; full subcategory; Ding injective module; Ding compatible module

Gorenstein同调代数的研究可追溯到Auslander等对双边诺特环上有限生成模的 G -维数的研究。（剩余17340字）