Every semiprimary ring is the endomorphism ring of a projective module over a quasihereditary ring

When is the ring of real measurable functions a hereditary ring?

‎Let $M(X‎, ‎mathcal{A}‎, ‎mu)$ be the ring of real-valued measurable functions‎ ‎on a measure space $(X‎, ‎mathcal{A}‎, ‎mu)$‎. ‎In this paper‎, ‎we characterize the maximal ideals in the rings of real measurable functions‎ ‎and as a consequence‎, ‎we determine when $M(X‎, ‎mathcal{A}‎, ‎mu)$ is a hereditary 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

Projectivity and flatness over the endomorphism ring of a finitely generated module

Let A be a ring, and Λ a finitely generated A-module. We give necessary and sufficient conditions for projectivity and flatness of a module over the endomorphism ring of Λ.

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...