Abstract

Let $R$ be a commutative local ring and let $C$ be a semidualizing $R$-module. In [E. Tavasoli, M. Salimi, Relative Matlis duality with respect to a semidualizing module, Bull. Math. Soc. Sci. Math. Roum., Nouv. Sér., 66(114), 4 (2023), 433--444], the notion of relative Matlis duality with respect to $C$, and $C$-Matlis reflexive modules are introduced, which generalized the notions of Matlis duality and Matlis reflexive modules. In this paper, we investigate conditions under which the $R$-modules ${\rm Ext}^{i\geqslant 0}_R{(M,N)}$ and ${\rm Tor}^R_{i\geqslant 0}{(M,N)}$ become $C$-Matlis reflexive, where $M$ and $N$ are $R$-modules. In addition, we deal with the isomorphic modules to the relative Matlis duality of $R$-modules ${\rm Ext}^{i\geqslant 0}_R{(M,N)}$, and ${\rm Tor}^R_{i\geqslant 0}{(M,N)}$ in the case that $M$ and $N$ are Matlis reflexive modules over the complete ring $R$.

Keywords: Semidualizing; Matlis duality; Matlis reflexive.

MSC: 13D05, 13D45, 18G20

DOI: 10.57016/MV-BFZe2402

Pages:  1--7