The main aim of this article is to study the relation between F-injective singularity and the
Frobenius closure of parameter ideals in Noetherian rings of positive characteristic. The …

In this paper, we explore the relation between the index of reducibility and the Hilbert
coefficients in local rings. Consequently, the main result of this study provides a …

Let M be a finitely generated module over a Noetherian ring R and N be a submodule. The
index of reducibility ir M (N) is the number of irreducible submodules that appear in an …

Let (R, m) be a Noetherian local ring and M a finitely generated R-module. Following IG
Macdonald [8], the set of all attached primes of the Artinian local cohomology module H mi …

Let $(R,\frak m) $ be a homomorphic image of a Cohen-Macaulay local ring and $ M $ a
finitely generated $ R $-module. We use the splitting of local cohomology to shed a new light …

In this paper, we investigate the relationship between the index of reducibility and Chern
coefficients for primary ideals. As an application, we give characterizations of a Cohen …

抄録 Let (R, $\mathfrak {m} $) be a commutative Noetherian local ring. A finitely generated R-
module M is called sequentially generalized Cohen-Macaulay module if there is a filtration …

On the uniform bound of the index of reducibility of parameter ideals of a module whose
polynomial type is at most one Page 1 Arch. Math. 101 (2013), 469–478 c© 2013 Springer …

Let be a Noetherian local ring and let M be a finitely generated R-module of dimension d.
Let be a system of parameters of M and let be a d-tuple of positive integers. In this paper we …

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