In this paper we introduce the concept of generalized Baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. We give some inequalities for the generalized Baer-invariant of a pair of finite groups, when ? is considered to be the Schur-Baer variety. Further, we present a sufficient condition under which the order of the generalized Baer-invariant of a pair of finite ...

in this paper, we give connection between the order of the generalized baer-invariant of a pair of finite groups and its factor groups, when ? is considered to be the specific variety. moreover, we give a necessary and sufficient condition in which the generalized baer-invariant of a pair of groups can be embedded into the generalized baer-invariant of pair of its factor groups.

A ringR is called generalized right Baer if for any non-empty subset S of R, the right annihilator rR(S ) is generated by an idempotent for some positive integer n. Generalized Baer rings are special cases of generalized PP rings and a generalization of Baer rings. In this paper, many properties of these rings are studied and some characterizations of von Neumann regular rings and PP rings are ...

in this paper we introduce the concept of generalized baer-invariant of a pair of groups with respect to two varieties ? and ? of groups. we give some inequalities for the generalized baer-invariant of a pair of finite groups, when ? is considered to be the schur-baer variety. further, we present a sufficient condition under which the order of the generalized baer-invariant of a pair of finite ...

Let Γ denote a distance-regular graph with diameter D ≥ 3. Assume Γ has classical parameters (D, b, α, β) with b < −1. Let X denote the vertex set of Γ and let A ∈ MatX(C) denote the adjacency matrix of Γ. Fix x ∈ X and let A ∈ MatX(C) denote the corresponding dual adjacency matrix. Let T denote the subalgebra of MatX(C) generated by A,A . We call T the Terwilliger algebra of Γ with respect to ...

We introduce and study the concept of $alpha $-semi short modules.Using this concept we extend some of the basic results of $alpha $-short modules to $alpha $-semi short modules.We observe that if $M$ is an $alpha $-semi short module then the dual perfect dimension of $M$ is $alpha $ or $alpha +1$.%In particular, if a semiprime ring $R$ is $alpha $-semi short as an $R$-module, then its Noetheri...

In this paper, a system for efficient removal of carbon dioxide by hollow fiber membranes is proposed. The system is compact, and it is very useful for application in the offshore energy industries. In particular, it is used to removing CO2 from the exhaust of power generation facilities on offshore platforms.The proposed dual membrane contactor contains two types of membranes (polypropylene me...

BACKGROUND Reports of the use of brainstem auditory evoked response (BAER) as a diagnostic modality in foals have been limited. HYPOTHESIS/OBJECTIVES To describe BAER findings and associated causes of hearing loss in foals. ANIMALS Study group 18 foals (15 neonatal, 3 nonneonatal), control group (5 neonatal foals). METHODS Retrospective. BAER records from the Clinical Neurophysiology Labo...

Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual o...