2025/04/24 by Rahimi, Ahad
#13C14 #13C15 #13D45 #18G40 #Commutative Algebra (math.AC) #FOS: Mathematics
paper · doi:10.48550/arxiv.2504.17217
Let A and B be commutative Noetherian algebras over an arbitrary field \Bbbk such that A ⊗_\Bbbk B is Noetherian. We consider ideals I and J of A and B, respectively, as well as nonzero finitely generated modules L and N over A and B, respectively. In this paper, we investigate certain algebraic properties of the A ⊗_\Bbbk B-module L⊗\Bbbk N, which are often inherited from the properties of the A-module L and the B-module N. Specifically, we provide characterizations for the Cohen-Macaulayness, generalized Cohen-Macaulayness, and sequentially Cohen-Macaulayness of L⊗\Bbbk N with respect to the ideal I ⊗_\Bbbk B + A ⊗_\Bbbk J, in terms of the corresponding properties for L and N with respect to I and J, respectively.