In this paper, we introduce and study a strict generalization of symmetric rings. We call ring $R$ \textit{`$P$-symmetric' } if for any $a,\, b,\, c\in R,\, abc=0$ implies $bac\in P(R)$, where $P(R)$ is the prime radical $R$. It shown that class $P$-symmetric rings lies between central generalized weakly Relations are provided some other known classes From an arbitrary ring, produce many families

The aim of this study is to provide a generalization prime vague Γ-ideals in Γ-rings by introducing non-symmetric 2-absorbing weakly complete commutative Γ-rings. A novel algebraic structure primary Γ-ideal Γ-ring presented ideal theory. approach K-vague are examined and the relation between level subset given. image inverse studied 1-1 inclusion-preserving correspondence theorem quotient R ind...

Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

According to Arnol’d and Sevryuk, a Hamiltonian vector field XH is said to be weakly reversible if φ∗XH = −XH for some germ φ of real analytic transformation with φ(0) = 0, while XH is reversible if additionally φ is an involution, i.e., φ = Id. One also says that α1, . . . , αn are non-resonant, if k · α ≡ k1α1 + · · · + knαn = 0 (3) for all integers kj with k = (k1, . . . , kn) = 0. The main ...

Delafossite CuFeO2 hexagonal platelets/rings and graphene composites were synthesized by a low temperature hydrothermal method. The formation mechanism of CuFeO2 hexagonal platelets/rings follows the combined effects of both GO and NaOH. The obtained composites as anode materials display a good battery performance with high reversible capacity, good rate capability and cyclic stability.

we show  that a projective maximal submodule of afinitely generated, regular, extending module is a directsummand. hence, every finitely generated, regular, extendingmodule with projective maximal submodules is semisimple. as aconsequence, we observe that every regular, hereditary, extendingmodule is semisimple. this generalizes and simplifies a result of  dung and   smith. as another consequen...

In this paper, we introduce and study graded weakly 1-absorbing prime ideals in commutative rings. Let \(G\) be a group \(R\) \(G\)-graded ring with nonzero identity \(1\neq0\). A proper ideal \(P\) of is called if for each nonunits \(x,y,z\in h(R)\) \(0\neq xyz\in P\), then either \(xy\in P\) or \(z\in P\). We give many properties characterizations ideals. Moreover, investigate under homomorph...

Let R be a commutative ring with nonzero identity. A proper ideal I of is said to 1-absorbing prime if xyz ∈ for some nonunits x, y, z R, then xy or I. It well known that ⇒ primary semi-primary ideal, is, the class ideals comes between classes and ideals. Also, above right arrows are not reversible. In this article, we characterize rings over which every prime. by comparing other classical such...

We study reversible polymerization of rings. In this stochastic process, two monomers bond and, as a consequence, two disjoint rings may merge into a compound ring or a single ring may split into two fragment rings. This aggregation-fragmentation process exhibits a percolation transition with a finite-ring phase in which all rings have microscopic length and a giant-ring phase where macroscopic...