The above topology is defined and studied on $ C (X) $, the ring of real-valued continuous
functions on a completely regular Hausdorff space $ X $. The minimal ideals and the socle …

Let CF (X) denote the socle of C (X). It is shown that X is a P-space if and only if C (X) is a ℵ0-
selfinjective ring or equivalently, if and only if is ℵ0-selfinjective. We also prove that X is an …

Our main aim in this article is to settle this question by showing that the above ring is never a
self-injective ring. Using a result of Osofsky [ll] and a result in [12] we immediately observe …

Introduction. Recently in [6], Theorem 4, it has been shown that if R is a self-~ njective
strongly regular rrng, then the power series ring R [[x]] is a duo ring (ie, every one-sided …

‎ 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 …

A frame $ L $ is called {\it coz-dense} if $\Sigma_ {coz (\alpha)}=\emptyset $ implies
$\alpha=\mathbf 0$. Let $\mathcal RL $ be the ring of real-valued continuous functions on a …

Let $ M (X,\mathcal {A},\mu) $ be the ring of real-valued measurable functionson a measure
space $(X,\mathcal {A},\mu) $. In this paper, we show that the maximal ideals of $ M …

We extend various properties from a direct summand X of a module M, whose complement
is semisimple, to its trace in M or to M itself. The case when MR= RR and the properties are …

We show that a projective maximal submodule of afinitely generated, regular, extending
module is a directsummand. Hence, every finitely generated, regular, extendingmodule with …

We prove that the following conditions for λ− BRS rings are equivalent: R is a λ− self-
injective; R is λ− linearly compact; If S∪ T is an orthogonal set in R with S∩ T=∅ and| S∪ …