نتایج جستجو برای: radical of a submodule
تعداد نتایج: 23284184 فیلتر نتایج به سال:
In this article, we develop the tool of saturation in the context of primary-like submodules of modules. We are particularly interested in relationships among the saturation of a primary-like submodule satisfying the primeful property and its radical. Furthermore, we provide sufficient conditions involving saturation and torsion arguments under which the radical of such a submodule is prime.
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}...
Let $R$ be a commutative ring with identity and let $M$ be an $R$-module. In this paper, we will introduce the secondary radical of a submodule $N$ of $M$ as the sum of all secondary submodules of $M$ contained in $N$, denoted by $sec^*(N)$, and explore the related properties. We will show that this class of modules contains the family of second radicals properly and can be regarded as a dual o...
The purpose of this paper is to introduce new concepts in a module  over ring , the first one called e*- small essential submodule, which generalization second concept called e*-radical submodule radical and last e* - hollow module. We will prove some properties all these concepts.
An R-module A is called GF-regular if, for each a ∈ A and r ∈ R, there exist t ∈ R and a positive integer n such that r(n)tr(n)a = r(n)a. We proved that each unitary R-module A contains a unique maximal GF-regular submodule, which we denoted by M GF(A). Furthermore, the radical properties of A are investigated; we proved that if A is an R-module and K is a submodule of A, then MGF(K) = K∩M GF(A...
Let M be a right R-module. We call M Rad-H-supplemented iffor each Y M there exists a direct summand D of M such that(Y + D)/D (Rad(M) + D)/D and (Y + D)/Y (Rad(M) + Y )/Y .It is shown that:(1) Let M = M1M2, where M1 is a fully invariant submodule of M.If M is Rad-H-supplemented, thenM1 andM2 are Rad-H-supplemented.(2) Let M = M1 M2 be a duo module and Rad--supplemented. IfM1 is radical M2-...
In this paper, we introduce the concept of a quasi-radical semi prime submodule. Throughout work, assume that is commutative ring with identity and left unitary R- module. A proper submodule called (for short Q-rad-semiprime), if for , ,and then . Where intersection all submodules
Using the notion of fuzzy small submodules of a module, we introduce the concept of fuzzy coessential extension of a fuzzy submodule of a module. We attempt to investigate various properties of fuzzy small submodules of a module. A necessary and sufficient condition for fuzzy small submodules is established. We investigate the nature of fuzzy small submodules of a module under fuzzy direct sum....
in recent years many researchers have been focused on interaction of small molecules with dna. dna is generally the primary intracellular of anticancer drugs, so the interaction between small molecules and dna can cause dna damage in cancer cells, blocking the division of cancer cells and resulting in cell death. the flavonoids are a large group of polyphenolic natural products that are widely ...
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