Let $R$ be a commutative ring with identity and $M$ be a finitely generated unital $R$-module. In this paper, first we give necessary and sufficient conditions that a finitely generated module to be a multiplication module. Moreover, we investigate some conditions which imply that the module $M$ is the direct sum of some cyclic modules and free modules. Then some properties of Fitting ideals o...

$r$-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.

let $r$ be a ring and $m$ a right $r$-module with $s=end_r(m)$. a module $m$ is called semi-projective if for any epimorphism $f:mrightarrow n$, where $n$ is a submodule of $m$, and for any homomorphism $g: mrightarrow n$, there exists $h:mrightarrow m$ such that $fh=g$. in this paper, we study sgq-projective and$pi$-semi-projective modules as two generalizations of semi-projective modules. a m...

let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

In the present paper, the concepts of module (uniform) approximate amenability and contractibility of Banach algebras that are modules over another Banach algebra, are introduced. The general theory is developed and some hereditary properties are given. In analogy with the Banach algebraic approximate amenability, it is shown that module approximate amenability and contractibility are the same ...

‎we say that a module $m$ is a emph{cms-module} if‎, ‎for every cofinite submodule $n$ of $m$‎, ‎there exist submodules $k$ and $k^{'}$ of $m$ such that $k$ is a supplement of $n$‎, ‎and $k$‎, ‎$k^{'}$ are mutual supplements in $m$‎. ‎in this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎in particular‎, ‎we prove tha...

In this paper, we define super Hilbert module and investigate frames in this space. Super Hilbert modules are  generalization of super Hilbert spaces in Hilbert C*-module setting. Also, we define frames in a super Hilbert module and characterize them by using of the concept of g-frames in a Hilbert C*-module. Finally, disjoint frames in Hilbert C*-modules are introduced and investigated.

‎We say that a module $M$ is a emph{cms-module} if‎, ‎for every cofinite submodule $N$ of $M$‎, ‎there exist submodules $K$ and $K^{'}$ of $M$ such that $K$ is a supplement of $N$‎, ‎and $K$‎, ‎$K^{'}$ are mutual supplements in $M$‎. ‎In this article‎, ‎the various properties of cms-modules are given as a generalization of $oplus$-cofinitely supplemented modules‎. ‎In particular‎, ‎we prove tha...

The sexual Fus3 MAP kinase module of yeast is highly conserved in eukaryotes and transmits external signals from the plasma membrane to the nucleus. We show here that the module of the filamentous fungus Aspergillus nidulans (An) consists of the AnFus3 MAP kinase, the upstream kinases AnSte7 and AnSte11, and the AnSte50 adaptor. The fungal MAPK module controls the coordination of fungal develop...