let $r$ be an infinite ring. here we prove that if $0_r$ belongs to ${x_1x_2cdots x_n ;|; x_1,x_2,dots,x_nin x}$ for every infinite subset $x$ of $r$, then $r$ satisfies the polynomial identity $x^n=0$. also we prove that if $0_r$ belongs to ${x_1x_2cdots x_n-x_{n+1} ;|; x_1,x_2,dots,x_n,x_{n+1}in x}$ for every infinite subset $x$ of $r$, then $x^n=x$ for all $xin r$.

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...

in this note we consider the notion of intuitionistic fuzzy (weak) dual hyper k-ideals and obtain related results. then we classify this notion according to level sets. after that we determine the relationships between intuitionistic fuzzy (weak) dual hyper k-ideals and intuitionistic fuzzy (weak) hyper k-ideals. finally, we define the notion of the product of two intuitionistic fuzzy (weak) du...

An original spectral study of the compressible hybrid lattice Boltzmann method (HLBM) on standard is proposed. In this framework, mass and momentum equations are addressed using (LBM), while finite difference (FD) schemes solve an energy equation. Both systems coupled with each other thanks to ideal gas equation state. This work aims at answering some questions regarding numerical stability suc...

We consider dynamical systems arising from iterating a morphism of a projective variety defined over the field of fractions of a discrete valuation ring. Our goal is to obtain information about the dynamical system over the field of fractions by studying the dynamical system over the residue field. In particular, we aim to bound the possible primitive periods for a periodic point. This is discu...

Abstract For a semisimple Lie algebra defined over discrete valuation ring with field of fractions K , we prove that any primitive ideal rational central character in the affinoid enveloping algebra, $$\widehat{U({\mathfrak {g}})_{K}}$$ U ( g )</...

Quantum teleportation is a primitive in several important applications, including quantum communication, computation, error correction, and networks. In this paper, we propose an optimal test for the performance of continuous-variable (CV) terms energy-constrained channel fidelity between ideal CV its experimental implementation. Work prior to ours considered suboptimal tests teleportation, foc...