Related papers: On minimal extensions of rings and applications
In [Y.~K.~Hu, K.~A.~Kopotun, X.~M.~Yu, Constr. Approx. 2000], the authors have obtained a characterization of best $n$-term piecewise polynomial approximation spaces as real interpolation spaces between $L^p$ and some spaces of bounded…
This article derives lower bounds on the supremal (strict) p-negative type of finite metric spaces using purely elementary techniques. The bounds depend only on the cardinality and the (scaled) diameter of the underlying finite metric…
Given a ring $R$, we study the bimodules $M$ for which the trivial extension $R\propto M$ is morphic. We obtain a complete characterization in the case where $R$ is left perfect, and we prove that $R\propto Q/R$ is morphic when $R$ is a…
Lusztig has given a construction of certain representations of reductive groups over finite local principal ideal rings of characteristic p, extending the construction of Deligne and Lusztig of representations of reductive groups over…
We introduce a notion of locally approximable continuous CR functions on locally closed subsets of reduced complex spaces, generalizing both holomorphic functions and CR functions on CR submanifolds. Under additional assumptions of…
We present an overview of some of our recent results on the existence of rays of minimal growth for elliptic cone operators and two new results concerning the necessity of certain conditions for the existence of such rays.
In the context of modeling biological systems, it is of interest to generate ideals of points with a unique reduced Groebner basis, and the first main goal of this paper is to identify classes of ideals in polynomial rings which share this…
We show that the splinter property ascends along regular residue field extensions, and along arbitrary regular maps in equal characteristic. We also study the splinter property of non-Noetherian rings, especially those related to…
We provide uniqueness results for compact minimal submanifolds in a large class of Riemannian manifolds of arbitrary dimension. In the case compact and Cartan-Hadamard manifolds we obtain general results for these submanifolds. Several…
Every reduced ring $R$ has a natural partial order defined by $a\le b$ if $a^2=ab$; it generalizes the natural order on a boolean ring. The article examines when $R$ is a lower semi-lattice in this order with examples drawn from weakly Baer…
We expose a rather simple and direct approach to the structure theory of prime PI-rings ("Posner's theorem"), based on fundamental properties of the extended centroid of a prime ring.
We show that diagonalization, products and lower truncations preserve the property of being a denormalized volume polynomial. We also discuss an application to poset inequalities.
The paper studies some properties of the ring of integer-valued quasi-polynomials. On this ring, theory of generalized Euclidean division and generalized GCD are presented. Applications to finite simple continued fraction expansion and…
We consider a fractional version of Gauss capillarity energy. A suitable extension problem is introduced to derive a boundary monotonicity formula for local minimizers of this fractional capillarity energy. As a consequence, blow-up limits…
We study the boundary behavior of the so-called ring $Q$-mappings obtained as a natural generalization of mappings with bounded distortion. We establish a series of conditions imposed on a function $Q(x)$ for the continuous extension of…
We discuss some extensions and refinements of the variance bounds for both real and complex numbers. The related bounds for the eigenvalues and spread of a matrix are also derived here.
We investigate bicomplex analogues of fundamental notions from classical algebraic number theory. In particular, we show that the primitive element theorem admits a natural generalization to bicomplex extensions, giving rise to two distinct…
We introduce the concept of functions of locally bounded variation on abstract Wiener spaces and study their properties. Some nontrivial examples and applications to stochastic analysis are also discussed.
Splint of root system of simple Lie algebra appears naturally in the study of (regular) embeddings of reductive subalgebras. It can be used to derive branching rules. Application of splint properties drastically simplifies calculations of…
We derive Moore-type upper bounds for regular simplicial complexes and present logarithmic lower bounds on their diameter based on minimum degree.