Let R be a commutative ring with identity and M an R–module. If M is either locally cyclic
projective or faithful multiplication then M is locally either zero or isomorphic to R. We …

All rings are commutative with identity and all modules are unital. Let R be a ring and M an R-
module. In our recent work we investigated faithful multiplication modules and the properties …

The associated ideal θ (M) and the trace ideal T (M) of a module M play analogous but
distinct roles in the study of multiplication and projective modules respectively. We further …

In this paper we study commutative rings $ R $ whose prime ideals are direct sums of cyclic
modules. In the case $ R $ is a finite direct product of commutative local rings, the structure …

Let be a commutative ring and an-module. Then is a multiplication module if for each
submodule of. The ideal of has proved useful in studying multiplication modules. We show …

Let R be a commutative ring with 1, and let M be a (left) unitary R-module. Following [2] we
say that M is F regular if each submodule of M is pure, and M is 2z regular if for each a EM …

Let R be a commutative ring with 1. If I is a finitely generated (fg) ideal in R, then I is a
projective ideal iff I is a multiplication ideal and ann (I) is generated by an idempotent [9] …

A famous theorem of commutative algebra due to IM Isaacs states that “if every prime ideal
of R is principal, then every ideal of R is principal”. Therefore, a natural question of this sort …

All rings are assumed to be associative and with nonzero identity element. Unless otherwise
stated all modules are unital right modules. Expressions such as “a Noetherian ring” mean …

Let R be a commutative ring. We determine the cyclic modules in the projectivity domain and
those in the injectivity domain of a simple R-module. An R-module M is called poor (p-poor) …