a polynomial   1 2 ( , , , ) n f x x x is called multilinear if it is homogeneous and linear in every one of its variables. in the present paper our objective is to prove the following result: let   r be a prime k-algebra over a commutative ring   k with unity and let 1 2 ( , , , ) n f x x x be a multilinear polynomial over k. suppose that   d is a nonzero derivation on r such that ...

We obtain a new $\varOmega $-result for the remainder term $\psi (x)-x$ of Beurling prime system which integers are very well-behaved in sense that $N(x)=ax + \mathrm O(x^\beta )$ some $a \gt 0$ and $\beta \lt 1/2$. As part

Let R <-* S be an embedding of associative noetherian rings such that 5 is finitely generated as a right Ä-module. There is a correspondence from the prime spectrum of S to the prime spectrum of R obtained by associating to a given prime ideal P of S the prime ideals of R minimal over P n R . The prime and primitive ideal theories for several specific noncommutative noetherian rings, including ...

The logarithmic coefficients play an important role for different estimates in the theory of univalent functions.Due to significance recent studies about coefficients, problem obtaining sharp bounds second Hankel determinant these that is $H_{2,1}(F_f/2)$ was paid attention. We recall if $f$ and $F$ are two analytic functions $\mathbb{D}$, function subordinate $F$, written $f(z)\prec F(z)$, the...

We present a (random) polynomial-time algorithm to generate a randomGaussian integer with the uniform distribution among those with norm at most N , along with its prime factorization. The method generalizes to finding a random ideal in the ring of integers of a quadratic number field together with its prime ideal factorization. We also discuss the analogous problem for higher degree number fie...

In this work, we use the $C^3P_{\,0}$ model to calculate decay widths of low lying charmonium $J^{PC}=1^{--}$ states, nominally $J/\psi(1S)$ and $\psi(2S)$, in following common channels: $\rho\,\pi$, $\omega\,\eta$, $\omega\,\eta^\prime$, $K^{\ast +}\,K^-$, 0}\,\bar{K}^0$, $\phi\,\eta$, $\phi\,\eta^\prime$.

In this work we study the monodromy group of covers $\varphi \circ \psi$ curves \linebreak $\mathcal{Y}\xrightarrow {\quad {\psi}} \mathcal{X} \xrightarrow \varphi} \mathbb{P}^{1}$, where $\psi$ is a $q$-fold cyclic \'etale cover and $\varphi$ totally ramified $p$-fold cover, with $p$ $q$ different prime numbers odd. We show that Galois $\mathcal{G}$ closure $\mathcal{Z}$ form $ \mathcal{G} = \...

In the p-th cyclotomic field Qpn , p a prime number, n ∈ N, the prime p is totally ramified and the only ideal above p is generated by ωn = ζpn − 1, with the primitive p-th root of unity ζpn = e 2πi pn . Moreover these numbers represent a norm coherent set, i.e. NQpn+1/Qpn(ωn+1) = ωn. It is the aim of this article to establish a similar result for the ray class field Kpn of conductor p over an ...

2. Primary ideals in C(X). C(X) denotes the ring of real-valued continuous functions on the topological space X, under ordinary pointwise addition and multiplication. By a primary ideal we mean an ideal which is contained in at most one maximal ideal. An O-ideal is an ideal / such that for each pair/i,/2G/ there exists eEI, depending on/i and f2, such that/<«=/.-, for i = l, 2 [7; 4]. A prime-l...

The aim of this paper is to study the behaviour of certain sequence of nonlinear Durrmeyer operators $ND_{n}f$ of the form $$(ND_{n}f)(x)=intlimits_{0}^{1}K_{n}left( x,t,fleft( tright) right) dt,,,0leq xleq 1,,,,,,nin mathbb{N}, $$ acting on bounded functions on an interval $left[ 0,1right] ,$ where $% K_{n}left( x,t,uright) $ satisfies some suitable assumptions. Here we estimate the rate...