Let $R$ be a commutative ring and $M$ an $R$-module. A submodule $N$ of is called d-submodule $($resp., fd-submodule$)$ if $\ann_R(m)\subseteq \ann_R(m')$ $\ann_R(F)\subseteq \ann_R(m'))$ for some $m\in N$ finite subset $F\subseteq N)$ $m'\in M$ implies that N.$ Many examples, characterizations, properties these submodules are given. Moreover, we use them to characterize modules satisfying Prop...

SUMMARY We present a tool called MRSD (Metabolic Route Search and Design) to search and design routes based on the weighted compound transform diagraph. The search submodule returns routes between a source and product compound within seconds in the network of one or multiple organisms based on data from KEGG. The design submodule designs a route from an appointed compound in an interactive mode...

A new submodule clustering method via sparse and lowrank representation for multi-way data is proposed in this paper. Instead of reshaping multi-way data into vectors, this method maintains their natural orders to preserve data intrinsic structures, e.g., image data kept as matrices. To implement clustering, the multi-way data, viewed as tensors, are represented by the proposed tensor sparse an...

‎Let $R$ be a domain with quotiont field $K$‎, ‎and‎ ‎let $N$ be a submodule of an $R$-module $M$‎. ‎We say that $N$ is‎ ‎powerful (strongly primary) if $x,yin K$ and‎ ‎$xyMsubseteq N$‎, ‎then $xin R$ or $yin R$ ($xMsubseteq N$‎ ‎or $y^nMsubseteq N$ for some $ngeq1$)‎. ‎We show that a submodule‎ ‎with either of these properties is comparable to every prime‎ ‎submodule of $M$‎, ‎also we show tha...

‎In this work‎, ‎we introduce the concept of classical 2-absorbing secondary modules over a commutative ring as a generalization of secondary modules and investigate some basic properties of this class of modules‎. ‎Let $R$ be a commutative ring with‎ ‎identity‎. ‎We say that a non-zero submodule $N$ of an $R$-module $M$ is a‎ ‎emph{classical 2-absorbing secondary submodule} of $M$ ...

Irreducible covariant tensor modules for the Lie supergroups GL(m/n) and the Lie superalgebras gl(m/n) and sl(m/n) are obtained through the use of Young tableaux techniques. The starting point is the graded permutation action, first introduced by Dondi and Jarvis, on V. The isomorphism between this group of actions and the symmetric group Sl enables the graded generalization of the Young symmet...