Let R be a commutative ring with identity , and M is unitary left R-module”, “A proper submodule E of an R-module called weakly quasi-prime if whenever r, s ∈ R, m M, 0 ≠ rsm implies that rm or sm E”. “We introduce the concept quasi 2-absorbing as generalization submodule”, where r,s,t ∈M 0≠ rstm rtm stm E. we study basic properties 2-absorbing. Furthermore, relationships other classes module a...

This paper proposes a code reuse mechanism called module embedding that enables the building of new modules from existing ones through inheritance, overriding of procedures, and overriding of types; the paper also describes an implementation scheme for this mechanism. Module embedding is beneficial when modules and classes are used in combination and need to be extended together, or when module...

Theorem. Let R be a Cohen-Macaulay ring (locally, always) 1 c R an ideal o f height at least 2, S the Rees ring of R with respect to I, and G = S /S I the associated graded ring. Assume that S and G are Cohen-Macaulay rings, and that S has a canonical module cos. Then G has a canonical module r and: (i) I f co s can be embedded into S such that cos (considered as an ideal now) is not contained ...

We state several conditions under which comultiplication and weak comultiplication modulesare cyclic and study strong comultiplication modules and comultiplication rings. In particular,we will show that every faithful weak comultiplication module having a maximal submoduleover a reduced ring with a finite indecomposable decomposition is cyclic. Also we show that if M is an strong comultiplicati...

This paper reports on a quasi-experiment in which quantitative methods (QM) are embedded within a substantive sociology module. Through measuring student attitudes before and after the intervention alongside control group comparisons, we illustrate the impact that embedding has on the student experience. Our findings are complex and even contradictory. Whilst the experimental group were less li...

In this paper, we define the new notion of quasi-prime ideal which generalizes at once both prime ideal and primary ideal notions. Then a natural topology on the set of quasi-prime ideals of a ring is introduced which admits the Zariski topology as a subspace topology. The basic properties of the quasi-prime spectrum are studied and several interesting results are obtained. Specially, it is pro...

Let $R$ be a ring, $sigma$ be an endomorphism of $R$ and $M_R$ be a $sigma$-rigid module. A module $M_R$ is called quasi-Baer if the right annihilator of a principal submodule of $R$ is generated by an idempotent. It is shown that an $R$-module $M_R$ is a quasi-Baer module if and only if $M[[x]]$ is a quasi-Baer module over the skew power series ring $R[[x,sigma]]$.

$r$-module. in this paper, we explore more properties of $max$-injective modules and we study some conditions under which the maximal spectrum of $m$ is a $max$-spectral space for its zariski topology.

Nakayama (Ann. of Math. 42, 1941) showed that over an artinian serial ring every module is a direct sum of uniserial modules. Hence artinian serial rings have the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals. A ring with the property that each right (left) ideal is a finite direct sum of quasi-injective right (left) ideals will be called a ...