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...

let $r$ be a commutative ring with identity and $m$ be a unitary$r$-module. the primary-like spectrum $spec_l(m)$ is thecollection of all primary-like submodules $q$ such that $m/q$ is aprimeful $r$-module. here, $m$ is defined to be rsp if $rad(q)$ isa prime submodule for all $qin spec_l(m)$. this class containsthe family of multiplication modules properly. the purpose of thispaper is to intro...

let g be a finite group and let $gk(g)$ be the prime graph of g. we assume that $n$ is an odd number. in this paper, we show that if $gk(g)=gk(b_n(p))$, where $ngeq 9$ and $pin {3,5,7}$, then g has a unique nonabelian composition factor isomorphic to $b_n(p)$ or $c_n(p)$ . as consequences of our result, $b_n(p)$ is quasirecognizable by its spectrum and also by a new proof, the validity of a con...

We report a quantum–classical hybrid scheme for factorization of bi-prime numbers (which are odd and square-free) using IBM’s quantum processors. The proposed here involves both classical optimization techniques adiabatic techniques, is build by extending previous [Pal et al., Pramana 92, 26 (2019) Xu Phys. Rev. Lett. 108, 130501 (2012)]. part the very general in sense that it can be implemente...

Algebraic geometry emerged from the study of subsets of C defined by polynomial equations, namely algebraic sets. Parallel to this, real algebraic geometry emerged from studying subsets of R defined by polynomial equations and inequalities, namely semi-algebraic sets. Like algebraic geometry, classical methods in real algebraic geometry provided useful but limited intuition on the relationship ...

Multicasting is a fundamental networking primitive utilized by numerous applications. This also holds true for cognitive radio networks (CRNs) which have been proposed as a solution to the problems that emanate from the static non-adaptive features of classical wireless networks. A prime application of CRNs is dynamic spectrum access (DSA), which improves the efficiency of spectrum allocation b...

Duan and Winter studied the one-shot zero-error classical capacity of a quantum channel assisted by quantum non-signalling correlations, and formulated this problem as a semidefinite program depending only on the Kraus operator space of the channel. For the class of classical-quantum channels, they showed that the asymptotic zero-error classical capacity assisted by quantum non-signalling corre...

Cognitive radio is one of the most promising technologies that resolves the problem of inefficient spectrum utilization by enabling secondary user to opportunistically utilize the unused licensed bands. The prime functionality of cognitive radio is spectrum sensing in which presence of the primary usersis accurately detected. In this paper various spectrum sensing methods are presented together...