Let R be a commutative ring with identity and let M unitary R-module. In this paper, we introduce the notion of weakly S-2-absorbing submodule. Suppose that S is multiplicatively closed subset R. A submodule P (P:R M)∩S=∅ said to if there exists an element s ∈ such whenever a,b∈R m∈M 0≠abm∈P, then sab∈(P: M) or sam∈P sbm∈P. We give characterizations, properties examples submodules.

Let $R$ be a commutative ring with identity. An ideal $I$ of a ring $R$is called an annihilating ideal if there exists $rin Rsetminus {0}$ such that $Ir=(0)$ and an ideal $I$ of$R$ is called an essential ideal if $I$ has non-zero intersectionwith every other non-zero ideal of $R$. Thesum-annihilating essential ideal graph of $R$, denoted by $mathcal{AE}_R$, isa graph whose vertex set is the set...

The notions of pure ideals and pure submodules play an important role in the study of rings and their module categories. In this paper, we introduce right t-pure fuzzy ideals and pure fuzzy submodules of an R-module. We establish their basic properties, and use them to obtain fuzzy theoretic characterizations of right weakly regular rings. Among other results, we prove that a ring R is right we...

In this work, some properties of amply weak essential supplemented modules are investigated. Let M be a projective and weakly module. Then every finitely M-generated module is supplemented. R any ring. if only generated R-module an e-supplement submodule in

Abstract In this study, we aim to introduce the concepts of 1-absorbing prime submodules and weakly a unital module over noncommutative ring with nonzero identity. This is new class between (weakly submodules) 2-absorbing submodules). Let R be identity $$1\ne 0$$ 1 ≠ 0 </mml:m...

Weakly-interacting massive particles (WIMPs) annihilating in the center of the Sun or the Earth may give rise to energetic neutrinos which might be discovered by astronomical neutrino detectors. The angular distribution of the neutrino-induced muons is considered in detail via Monte Carlo simulations. It is shown that large underground Čerenkov neutrino telescopes might be able to extract the W...

let $r$ be a commutative ring with identity. an ideal $i$ of a ring $r$is called an annihilating ideal if there exists $rin rsetminus {0}$ such that $ir=(0)$ and an ideal $i$ of$r$ is called an essential ideal if $i$ has non-zero intersectionwith every other non-zero ideal of $r$. thesum-annihilating essential ideal graph of $r$, denoted by $mathcal{ae}_r$, isa graph whose vertex set is the set...

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 pr...

Let R be a commutative ring with identity. An ideal I of a ring R is called an annihilating ideal if there exists r ∈ R \ {0} such that Ir = (0) and an ideal I of R is called an essential ideal if I has non-zero intersection with every other non-zero ideal of R. The sum-annihilating essential ideal graph of R, denoted by AER, is a graph whose vertex set is the set of all non-zero annihilating i...