On the ring of endomorphisms of an indecomposable injective module over a Prüfer ring

Rigid Resolution of a Finitely Generated Module Over a Regular Local Ring

IRRELEVANT ATTACHED PRIME IDEALS OF A CERTAIN ARTINIAN MODULE OVER A COMMUTATIVE RING

Let M be an Artinian module over the commutative ring A (with nonzero identity) and a p spec A be such that a is a finitely generated ideal of A and aM = M. Also suppose that H = H where H. = M/ (0: a )for i

Ring endomorphisms with nil-shifting property

Cohn called a ring $R$ is reversible if whenever $ab = 0,$ then $ba = 0$ for $a,bin R.$ The reversible property is an important role in noncommutative ring theory‎. ‎Recently‎, ‎Abdul-Jabbar et al‎. ‎studied the reversible ring property on nilpotent elements‎, ‎introducing‎ the concept of commutativity of nilpotent elements at zero (simply‎, ‎a CNZ ring)‎. ‎In this paper‎, ‎we extend the CNZ pr...

Gröbner Basis and Indecomposable Modules over a like Dedekind Ring

Using Gröbner Basis, we introduce a general algorithm to determine the additive structure of a module, when we know about it using indirect information about its structure. We apply the algorithm to determine the additive structure of indecomposable modules over ZCp, where Cp is the cyclic group of order a prime number p, and the p−pullback {Z→ Zp ← Z} of Z⊕Z.

The Extended Centralizer of a Ring over a Module

In a recent paper,1 K. Asano gave a new proof of the theorem that a domain of integrity has a right quotient ring if and only if every pair of nonzero elements has a common nonzero right multiple. His method of proof is used in the present work to extend the centralizer of a ring over a module to a system of semi-endomorphisms of the module. From this extension, necessary and sufficient conditi...