The Zygmund sums of a function $f\in L_{1}$ are trigonometric polynomials the form $$Z^{s}_{n-1}(f;t):=\frac{a_{0}}{2}+\sum_{k=1}^{n-1}\Big(1-\big(\frac{k}{n}\big)^{s}\Big) \big(a_{k}(f)\cos kt+b_{k}(f)\sin kt\big), s>0,$$ where $a_{k}(f)$ and $b_{k}(f)$ Fourier coefficients $f$. We establish exact-order estimates uniform approximations by $Z^{s}_{n-1}$ $2\pi$-periodic continuous functions f...

let $l$ be a completely regular frame and $mathcal{r}l$ be the ringof continuous real-valued functions on $l$. we study the frame$mathfrak{o}(min(mathcal{r}l))$ of minimal prime ideals of$mathcal{r}l$ in relation to $beta l$. for $iinbeta l$, denoteby $textit{textbf{o}}^i$ the ideal${alphainmathcal{r}lmidcozalphain i}$ of $mathcal{r}l$. weshow that sending $i$ to the set of minimal prime ideals...

Introduction. L. Fuchs [2 ] has given for Noetherian rings a theory of the representation of an ideal as an intersection of primal ideals, the theory being in many ways analogous to the classical Noether theory. An ideal Q is primal if the elements not prime to Q form an ideal, necessarily prime, called the adjoint of Q. Primary ideals are necessarily primal, but not conversely. Analogous resul...

We study prime and primitive ideals in a uniied setting applicable to quanti-zations (at nonroots of unity) of n n matrices, of Weyl algebras, and of Euclidean and symplectic spaces. The framework for this analysis is based upon certain iterated skew polynomial algebras A over innnite elds k of arbitrary characteristic. Our main result is the veriication, for A, of a characterization of primiti...

A left almost semigroup (LA-semigroup) or an Abel-Grassmann’s groupoid (AG-groupoid) is investigated in several papers. In this paper we have discussed ideals in LA-semigroups. Specifically, we have shown that every ideal in an LA-semigroup S with left identity e is prime if and only if it is idempotent and the set of ideals of S is totally ordered under inclusion. We have shown that an ideal o...

We introduce the notion of n -homoderivation on a ring id="M3"> ℜ and show that semiprime id="M4"> must have nontrivial central ideal if it admits an appropriate id="M5"> which is centralizing some one-sided ideal. Under similar hypotheses, we prove commutativity in prime rings.

Our main subject is to study the action of the Hecke operators Tl on the Jacobian J of the modular curve X0(N). We consider the Hecke algebra T, i.e. the subring of End(J) generated by the Tl and the involution ω and define the Eisenstein ideal I ⊂ T as the ideal generated by 1 +ω and 1 + l−Tl, l prime 6= N . The Eisenstein quotient of J is the quotient J̃ := J/aJ where a denotes the kernel of t...

If A is a subset of Z, then the n-th characteristic ideal of A is the fractional ideal of Z consisting of 0 and the leading coe cients of polynomials in Q[x] of degree no more than n which are integer-valued on A. The valuative capacity with respect to a prime p of A is a measure of the rate of growth of the p-adic part of these characteristic ideals of A and is defined, for a given p, to be th...

In this paper, we introduce the notions of intuitionistic fuzzy prime (resp. strongly prime and semiprime) bi-ideals of a semigroup. By using these ideas we characterize those semigroups for which each intuitionistic fuzzy bi-ideal is semiprime and strongly prime. Key words: Intuitionistic fuzzy set; intuitionistic fuzzy bi-ideal; intuitionistic fuzzy prime (resp. strongly prime and semiprime) ...