In this paper, we give some generalized categories of topological spaces in terms of monotone operators and investigate some categorical properties of them. In particular, we present some equivalent categories of generalized ...

In this paper, it is shown that $ (mathcal{V}, mathfrak{X}) $ is a Schur pair if and only if the Baer-invariant of an $mathfrak{X}$-group with respect to $ mathcal{V}$ is an $mathfrak{X}$-group. Also, it is proved that a ...

Terms like commutativity degree, non-commuting graph and isoclinism are far well-known for much of the group theorists nowadays. There are so many papers about each of these concepts and also about their relationships in ...

Let $M$ be a module over a ring $R$. We call $M$,$delta$-$H$-supplemented provided for every submodule $N$ of $M$ there is a direct summand $D$ of $M$ such that $M=N+X$ if and only if $M=D+X$ for every submodule $X$ of $M$ ...

In this paper, we define the notion of strongly annihilating-submodule graph of modules. This graph is a straightforward common generalization of the annihilating-submodule graph  and the annihilating-ideal graph. In ...

Cofiniteness of the generalized local cohomology modules $H^{i}_{mathfrak{a}}(M,N)$ of two $R$-modules $M$ and $N$ withrespect to an ideal $mathfrak{a}$ is studied for some $i^{,}s$ witha specified property. ...

Let $(R,mathfrak{m})$ be a Noetherian local ring, $M$ a finitely generated $R$-module, and $mathfrak{a}$ an ideal of $R$. We define the $mathfrak{a}$-minimum dimension $d(mathfrak{a},M)$ of $M$ by $$d(mathfrak{a},M)=Min{dim ...

We will study modules whose cofinite submodules have weak generalized-$delta$-supplements.  We attempt to investigate some properties of cofinitely weak generalized $delta$-supplemented modules.  We will prove for a module ...