Introduction. Fix a base field k. The quantized coordinate ring of n×n matrices over k, denoted by q(Mn(k)), is a deformation of the classical coordinate ring of n×n matrices, (Mn(k)). As such, it is a k-algebra generated by n2 indeterminates Xij , for 1 ≤ i,j ≤ n, subject to relations which we state in (1.1). Here, q is a nonzero element of the field k. When q = 1, we recover (Mn(k)), which is...

in this paper, various elementary properties of vague rings are obtained. furthermore, the concepts of vague subring, vague ideal, vague prime ideal and vague maximal ideal are introduced, and the validity of some relevant classical results in these settings are investigated.

We consider the quantum evolution [Formula: see text] of a Gaussian coherent state localized close to classical text], where denotes self-adjoint realization formal Hamiltonian with derivative Dirac’s delta distribution at and real parameter. show that in semi-classical limit such can be approximated (with respect text]-norm, uniformly for any away from collision time) by is suitable extension ...

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 ...

‎‎Let $R$ be a commutative ring with identity and let $M$ be an $R$-module‎. ‎We define the primary spectrum of $M$‎, ‎denoted by $mathcal{PS}(M)$‎, ‎to be the set of all primary submodules $Q$ of $M$ such that $(operatorname{rad}Q:M)=sqrt{(Q:M)}$‎. ‎In this paper‎, ‎we topologize $mathcal{PS}(M)$ with a topology having the Zariski topology on the prime spectrum $operatorname{Spec}(M)$ as a sub...

It is shown that the convenient processing facilities of digital signals varying in a finite range amplitudes are non-binary Galois fields, numbers which elements equal to prime numbers. Within choosing sampling interval corresponding such field, it becomes possible construct field Fourier transform, distinctive feature exact correspondence with ranges variation original signal and its spectrum...

We construct the centralizer resolution of the spectrum EhS 1 2 in the category of K(2)-local spectra at the prime 2. We use the associated tower of fibrations to realize the duality resolution to a tower of fibrations whose limit is the spectrum EhS 1 2 . We also compute the Adams-Novikov spectral sequence for the spectrum tmf without assuming the ring structure on the spectrum and compute π∗E...

In this paper we defined prime ideal and maximal ideal and proved several properties of these. We have discussed the space of prime ideals of a C-algebra A with respect to the hull-kernel topology, which is called the prime spectrum of A and denoted by Spec A. It is also proved that Spec A is a T0 space.

We find the nonabelian finite simple groups with order prime divisors not exceeding 1000. More generally, we determine the sets of nonabelian finite simple groups whose maximal order prime divisor is a fixed prime less than 1000. Our results are based on calculations in the computer algebra system GAP.