a module $m$ is called $emph{h}$-cofinitely supplemented if for every cofinite submodule $e$ (i.e. $m/e$ is finitely generated) of $m$ there exists a direct summand $d$ of $m$ such that $m = e + x$ holds if and only if $m = d + x$, for every submodule $x$ of $m$. in this paper we study factors, direct summands and direct sums of $emph{h}$-cofinitely supplemented modules. let $m$ be an $emph{h}$...

In this paper we continue to study the strongly annihilating-submodule graph. addition providing more properties of graph, compare extensively graph with

In this paper, a modified submodule (MSM) method is proposed to reduce capacitor voltage fluctuation by integrating bidirectional buck-boost type active power decoupling (APD) circuit into each SM for the low-frequency operation of converter system. The MSM-MMC can be significantly reduced compared conventional SMs with same capacitance transferring ripple components auxiliary energy storage ca...

let $r$ be a commutative ring and let $m$ be an $r$-module. in this article, we introduce the concept of the zariski socles of submodules of $m$ and investigate their properties. also we study modules with noetherian second spectrum and obtain some related results.