let $r$ be an arbitrary ring and $t$ be a submodule of an $r$-module $m$. a submodule $n$ of $m$ is called $t$-small in $m$ provided for each submodule $x$ of $m$, $tsubseteq x+n$ implies that $tsubseteq x$. we study this mentioned notion which is a generalization of the small submodules and we obtain some related results.

Let $R$ be a commutative ring and let $M$ be an $R$-module. We define the small intersection graph $G(M)$ of $M$ with all non-small proper submodules of $M$ as vertices and two distinct vertices $N, K$ are adjacent if and only if $Ncap K$ is a non-small submodule of $M$. In this article, we investigate the interplay between the graph-theoretic properties of $G(M)$ and algebraic properties of $M...

let $r$ be a commutative ring and let $m$ be an $r$-module. we define the small intersection graph $g(m)$ of $m$ with all non-small proper submodules of $m$ as vertices and two distinct vertices $n, k$ are adjacent if and only if $ncap k$ is a non-small submodule of $m$. in this article, we investigate the interplay between the graph-theoretic properties of $g(m)$ and algebraic properties of $m...

We study the exterior depth of an E-module and its exterior generic annihilator numbers. For the exterior depth of a squarefree E-module we show how it relates to the symmetric depth of the corresponding S-module and classify those simplicial complexes having a particular exterior depth in terms of their exterior shifting. We define exterior annihilator numbers analogously to the annihilator nu...

Let $R$ be an arbitrary ring and $T$ be a submodule of an $R$-module $M$. A submodule $N$ of $M$ is called $T$-small in $M$ provided for each submodule $X$ of $M$, $Tsubseteq X+N$ implies that $Tsubseteq X$. We study this mentioned notion which is a generalization of the small submodules and we obtain some related results.

Primary-like and weakly primary-like submodules are two new generalizations of primary ideals from rings to modules. In fact, the class of primary-like submodules of a module lie between primary submodules and weakly primary-like submodules properly. In this note, we show that these three classes coincide when their elements are submodules of a multiplication module and satisfy the primeful pro...

The LOMOPLAN (LOcal MOnoPLane ANnihilator) lter in three dimensions is a deconvolution lter that takes a volume in and produces two volumes out. The x-output volume results from a rst order prediction-error lter on the x-axis, and the y-output volume is likewise on the y-axis. Synthetic data studies are promising.