let $a$ be a $c^*$-algebra and $e$ be a left hilbert $a$-module. in this paper we define a product on $e$ that making it into a banach algebra and show that under the certain conditions $e$  is arens regular. we also study the relationship between derivations of $a$ and $e$.

the main objective of this study is to swing krull intersection theorem in primary decomposition of rings and modules to the primary decomposition of soft rings and soft modules. to fulfill this aim several notions like soft prime ideals, soft maximal ideals, soft primary ideals, and soft radical ideals are introduced for a soft ring over a given unitary commutative ring. consequently, the p...

let r be a commutative ring with identity. let n and k be two submodules of a multiplication r-module m. thenn=im and k=jm for some ideals i and j of r. the product of n and k denoted by nk is defined by nk=ijm. inthis paper we characterize some particular cases of multiplication modules by using the product of submodules.

Introduction. A module over a ring will be said to be locally projective if and only if every finitely generated submodule is projective. As will be shown (7.14), it readily follows from known facts that if M is a locally projective module over a regular ring R, then the set L(M, R) of all finitely generated submodules of M is a relatively complemented modular lattice. This paper is concerned w...

In the present paper for two $mathfrak{A}$-module Banach algebras $A$ and $B$, we investigate relations between $varphi$-$mathfrak{A}$-module approximate amenability of $A$, $psi$-$mathfrak{A}$-module approximate amenability of $B$, and $varphioplus psi$-$mathfrak{A}$-module approximate amenability of $Aoplus B$ ($l^1$-direct sum of $A$ and $B$), where $varphiin$ Hom$_{mathfrak{A}}(A)$ and $psi...

Deciding inseparability of description logic knowledge bases (KBs) with respect to conjunctive queries is fundamental for many KB engineering and maintenance tasks including versioning, module extraction, knowledge exchange and forgetting. We study the combined and data complexity of this inseparability problem for fragments of Horn-ALCHI, including the description logics underpinning OWL 2 QL ...

Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.

Results on the finiteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some finite crossed modules are given, using crossed complex methods.

Results on the niteness of induced crossed modules are proved both algebraically and topologically. Using the Van Kampen type theorem for the fundamental crossed module, applications are given to the 2-types of mapping cones of classifying spaces of groups. Calculations of the cohomology classes of some nite crossed modules are given, using crossed complex methods.