Related papers: Minimal ring extensions of the integers exhibiting…

Let $M(d,\chi)$ with $(d,\chi)=1$ be the moduli space of semistable sheaves on $\mathbb{P}^2$ supported on curves of degree $d$ and with Euler characteristic $\chi$. The cohomology ring $H^*(M(d,\chi),\mathbb{Z})$ of $M(d,\chi)$ is…

We characterize minimal measurement setups for validating the quantum coherence of an unknown quantum state. We show that for a $d$-level system, the optimal strategy consists of measuring $d$ orthonormal bases such that each measured basis…

We study quasiperiodically forced circle endomorphisms, homotopic to the identity, and show that under suitable conditions these exhibit uncountably many minimal sets with a complicated structure, to which we refer to as `strangely…

The generating series of the Bass numbers $\mu^i_R=\mathrm{rank}_k \mathrm{Ext}^i_R(k,R)$ of local rings $R$ with residue field $k$ are computed in closed rational form, in case the embedding dimension $e$ of $R$ and its depth $d$ satisfy…

In this paper we give a compact presentation of the theory of abstract spaces for convolutional codes and convolutional encoders, and show a connection between them that seems to be missing in the literature. We use it for a short proof of…

A minimum depth d^I(S --> R) is assigned to a ring homomorphism S --> R and a R-R-bimodule I. The recent notion of depth of a subring d(S,R)in a paper by Boltje-Danz-Kuelshammer is recovered when I = R and S --> R is the inclusion mapping.…

We study the arithmetic of monoids of regular elements of commutative rings with zero-divisors. Our focus is on Krull rings and on some of their generalizations (such as weakly Krull rings and C-rings). We establish sufficient conditions…

Classical realism demands that system properties exist independently of whether they are measured, while noncontextuality demands that the results of measurements do not depend on what other measurements are performed in conjunction with…

The Kochen-Specker no-go theorem established that hidden-variable theories in quantum mechanics necessarily admit contextuality. This theorem is formally stated in terms of the partial Boolean algebra structure of projectors on a Hilbert…

Let $R$ be a regular ring of dimension $d$ and $L$ be a $c$-divisible monoid. If ${K}_1{Sp}(R)$ is trivial and $k \geq d+2,$ then we prove that the symplectic group ${Sp}_{2k}(R[L])$ is generated by elementary symplectic matrices over…

We show that high Veronese subrings of any commutative graded ring have a Grobner basis with all relations of degree 2. (The d-th Veronese subring of a ring A_0 + A_1 + A_2 + ... is the ring A_0 + A_d + A_{2d} + ...; ``high'' means we take…

We obtain lower bounds on the rank of the kappa ring of the Delign-Mumford compactification of the moduli space of curves in different degrees. For this purpose, we introduce a quotient of the kappa ring, the combinatorial kappa ring, and…

In this note we study the distribution of the subrings of $\mathbb Z[t]/(t^4)$ and prove two results. The first result gives an asymptotic formula for the number of subrings of $\mathbb Z[t]/(t^4)$ of bounded index. The method of proof of…

We prove that the Schubert structure constants of the quantum $K$-theory ring of any minuscule flag variety or quadric hypersurface have signs that alternate with codimension. We also prove that the powers of the deformation parameter $q$…

In this paper we study contravariant functors from the category of rings to the category of sets whose restriction to the full subcategory of commutative rings is isomorphic to the prime spectrum functor Spec. The main result reveals a…

We construct minimum-uncertainty states and a non-negative quasi probability distribution for quantum systems on a finite-dimensional space. We reexamine the theorem of Massar and Spindel for the uncertainty relationof the two unitary…

The interplay between symmetry, entanglement and correlation is an interesting and important topic in quantum many-body physics. Within the framework of matrix product states, in this paper we study the minimal entanglement and correlation…

We review and extend recent findings of Godsil and Zaks, who published a constructive coloring of the rational unit sphere with the property that for any orthogonal tripod formed by rays extending from the origin of the points of the…

The theory of small cancellation groups is well known. In this paper we introduce the notion of Group-like Small Cancellation Ring. This is the main result of the paper. We define this ring axiomatically, by generators and defining…

We study Schmidt rank for a vector (i.e., a pure state) and Schmidt number for a mixed state which are entanglement measures. We show that if a subspace of a certain bipartite system contains no vector of Schmidt rank $\leqslant k$, then…