Some descriptions of linked ideals in a commutative Notherian ring $ R $ are provided in
terms of the Associated prime ideals of $ R $. Then, among other things, we make some …

In this paper, we introduce generalized Gorenstein local (GGL) rings. The notion of GGL
rings is a natural generalization of the notion of almost Gorenstein rings, which can thus be …

Let A and B be commutative rings with unity, f: A→ B a ring homomorphism, and J an ideal of
B. Then the subring A⋈ f J:={(a, f (a)+ j)| a∈ A and j∈ J} of A× B is called the amalgamation …

Let R be a commutative Noetherian ring and let I be an ideal of R. In this paper, we study the
amalgamated duplication ring R⋈ I which is introduced by D'Anna and Fontana. It is shown …

Inspired by the works in linkage theory of ideals, we define the concept of linkage of ideals
over a module. Several known theorems in linkage theory are improved or recovered by …

Let (R,m) be a Noetherian local ring which is a quotient of a Gorenstein local ring. Let M be a
finitely generated R-module. In this paper, we study the structure of the canonical module …

We study the class of one-dimensional Cohen–Macaulay local rings with canonical
reductions, ie, admit canonical ideals which are reductions of the maximal ideals, show that …

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 …

Let $ R $ be a commutative noetherian local ring, and let $ M $ be a finitely generated $ R $-
module. Inspired by works of Vasconcelos and Briggs on characterization of complete …

Let (R, m) be a Noetherian local ring and M a finitely generated R-module. In this paper, we
study some invariants of the idealization R⋉ M of R and M such as the polynomial type …