We study Serre’s condition for tensor products of modules over a commutative noetherian local ring . Specifically, we consider the following question. For finitely generated -modules and , either of which is -Tor-rigid, if the tensor product satisfies , then does hold for all ? The aim of this paper is to give an affirmative answer to this question if we assume local freeness and Serre’s condition on modules. As applications, we recover several known results.
"SERRE’S CONDITION FOR TENSOR PRODUCTS AND N-TOR-RIGIDITY OF MODULES." J. Commut. Algebra 15 (1) 55 - 63, Spring 2023. https://doi.org/10.1216/jca.2023.15.55