Monic modules and semi-Gorenstein-projective modules
Monic modules and semi-Gorenstein-projective modules
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DOI：
10.1016/j.jpaa.2022.107181
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发表时间：
2022-08
影响因子：
0.8
通讯作者：
Pu Zhang
中科院分区：
文献类型：
--
作者：
Pu Zhang
The category gp (Λ) of Gorenstein-projective modules over tensor algebra Λ= A⊗ k B can be described as the monomorphism category mon (B, gp (A)) of B over gp (A). In particular, Gorenstein-projective Λ-modules are monic. In this paper, we find the similar relation between semi-Gorenstein-projective Λ-modules and A-modules, via monic modules, namely, mon (B, A⊥)= mon (B, A)∩ Λ⊥. Using this, it is proved that if A is weakly Gorenstein, then Λ is weakly Gorenstein if and only each semi-Gorenstein-projective Λ-modules are monic; and that if B= k Q with Q a finite acyclic quiver, then Λ is weakly Gorenstein if and only if A is weakly Gorenstein. However, this relation itself does not answer the question whether there exist double semi-Gorenstein-projective Λ-modules which are not monic. Using the recent discovered examples of double semi-Gorenstein-projective A-modules which are not torsionless, we positively answer this question, by explicitly constructing a class of double semi-Gorenstein-projective T 2 (A)-modules with one parameter such that they are not monic, and hence not torsionless. The corresponding results are obtained also for the monic modules and semi-Gorenstein-projective modules over the triangular matrix algebras given by bimodules.
