In this paper, we investigate the maximal Cohen–Macaulay property of tensor products of
modules, and then give criteria for projectivity of modules in terms of vanishing of Ext …

Let R be a commutative Noetherian local ring and M, N be finitely generated R-modules. We
prove a number of results of the form: if Hom R (M, N) has some nice properties and Ext R …

Over an arbitrary commutative ring, correspondences among three sets, the set of trace
ideals, the set of stable ideals, and the set of birational extensions of the base ring, are …

In this article, we introduce an invariant of Cohen-Macaulay local rings in terms of the
reduction number of canonical ideals. The invariant can be defined in arbitrary Cohen …

The Cohen–Macaulay type of idealizations of maximal Cohen–Macaulay modules over
Cohen–Macaulay local rings is closely explored. There are two extremal cases, one of …

We develop the theory of trace modules up to isomorphism and explore the relationship
between preenveloping classes of modules and the property of being a trace module …

In this paper, we study Noetherian local rings R having a finite number of trace ideals. We
proved that such rings are of dimension at most two. Furthermore, if the integral closure of …

In the present paper we investigate reflexive modules over the endomorphism algebras of
reflexive trace ideals in a one-dimensional Cohen-Macaulay local ring. The main theorem …

Abstract Let I (≠ A) be an ideal of ad-dimensional Noetherian local ring A with ht AI≥ 2,
containing a non-zerodivisor. The problem of when the ring I: I= End AI is Gorenstein is …

The notion of commutative rings is important in singularity theory, and it is deeply related to
various algebraic areas, say, algebraic geometry, representation theory, invariant theory …