Related papers: Ideals on the Quantum Plane's jet space
Quantum rings can be characterized by a specific radius and ring width. For this rich class of physical systems, an accurate approximation for the exchange-hole potential and thus for the exchange energy is derived from first principles.…
Quantum networks offer a unifying set of opportunities and challenges across exciting intellectual and technical frontiers, including for quantum computation, communication, and metrology. The realization of quantum networks composed of…
Due to the recent groundbreaking developmentsof nanotechnologies,it became possible to create intrinsically quantum systems able to serve as high-directional antennas in THz, infrared and optical ranges. Actually, the quantum antennas,as…
In this paper, we collect the fundamental basic properties of jet modules in algebraic geometry and related properties of differential operators. We claim no originality but we want to provide a reference work for own research and the…
We consider the class of all commutative reduced rings for which there exists a finite subset T of A such that all projections on quotients by prime ideals of A are surjective when restricted to T. A complete structure theorem is given for…
A quantum robot is a mobile quantum system including an on bord quantum computer and ancillary systems, that interact with an environment of quantum systems. Quantum robots carry out tasks whose goals include carrying out measurements and…
In this paper we introduce and study a graph on the set of ideals of a commutative ring $R$. The vertices of this graph are non-trivial ideals of $R$ and two distinct ideals $I$ and $J$ are adjacent if and only $IJ=I\cap J$. We obtain some…
Brown and Goodearl stated a conjecture that provides an explicit description of the topology of the spectra of quantum algebras. The conjecture takes on a more explicit form if there exist separating Ore sets for all incident pairs of torus…
Let $O$ be an order in a quadratic number field $K$ with ring of integers $D$, such that the conductor $\mathfrak F = f D$ is a prime ideal of $O$, where $f\in\mathbb Z$ is a prime. We give a complete description of the $\mathfrak…
Quantum planes and a new quantum cylinder are obtained as quantization of Poisson homogeneous spaces of two different Poisson structures on classical Euclidean group E(2).
In this paper we investigate the question of normality for special monomial ideals in a polynomial ring over a field. We first include some expository sections that give the basics on the integral closure of a ideal, the Rees algebra on an…
We show that the theory of quantales and quantic nuclei motivate new results on star operations, semistar operations, semiprime operations, ideal systems, and module systems, and conversely the latter theories motivate new results on…
We establish the primary decomposition and uniqueness of primary decomposition for k-ideals in commutative Noetherian semirings.
In this survey article we give basic introduction to the theory of quantum families of maps. We begin with a general look at non-commutative (or "quantum") topology. Then we formulate all our results in this language. Existence of quantum…
Through the example of the quantum symplectic 4-sphere, we discuss how the notion of twisted spectral triple fits into the framework of quantum homogeneous spaces.
Quantum kernels are reproducing kernel functions built using quantum-mechanical principles and are studied with the aim of outperforming their classical counterparts. The enthusiasm for quantum kernel machines has been tempered by recent…
We show that every proper, dense ideal in a C*-algebra is contained in a prime ideal. It follows that a subset generates a C*-algebra as a not necessarily closed ideal if and only if it is not contained in any prime ideal. This allows us to…
At the primary level of reality as described by quantum field theory, a fundamental particle like an electron represents a stable, discrete, propagating excited state of its underlying quantum field. QFT also tells us that the lowest vacuum…
The purpose of this text is to set up a few basic notions concerning quantum graphs, to indicate some areas addressed in the quantum graph research, and to provide some pointers to the literature. The pointers in many cases are secondary,…
Quantum mechanics, one of the most successful theories in the history of science, was created to account for physical systems not describable by classical physics. Though it is consistent with all experiments conducted thus far, many of its…