Related papers: On minimal extensions of rings and applications
We prove that many of the results of the LMMP hold for $3$-folds over fields of characteristic $p>5$ which are not necessarily perfect. In particular, the existence of flips, the cone theorem, the contraction theorem for birational extremal…
Let $K$ be a local field with residue characteristic $p$ and let $L/K$ be a totally ramified extension of degree $p^k$. In this paper we show that if $L/K$ has only two distinct indices of inseparability then there exists a uniformizer…
In this paper, we study properties of polynomials over division rings. Moreover, we present formulas for finding roots of some polynomials
This paper investigates coherent-like conditions and related properties that a trivial extension might inherit from the ground ring over some classes of modules. It captures previous results dealing primarily with coherence, and also…
The main result of the paper is a flat extension theorem for positive linear functionals on *-algebras. The theorem is applied to truncated moment problems on cylinder sets, on matrices of polynomials and on enveloping algebras of Lie…
In this paper we consider a wide class of generalized Lipschitz extension problems and the corresponding problem of finding absolutely minimal Lipschitz extensions. We prove that if a minimal Lipschitz extension exists, then under certain…
In this paper we establish the relation between key polynomials (as defined in \cite{SopivNova}) and minimal pairs of definition of a valuation. We also discuss truncations of valuations on a polynomial ring $K[x]$. We prove that a…
In this paper, we study the small finitistic dimension of a commutative ring from the viewpoint of finitistic flat homological algebra. Using the class $FPR(R)$ of modules admitting finite projective resolutions, we investigate the…
It is shown that the extension of $\R$ by a generic smooth function restricted to the unit cube is o-minimal. The generalization to countably many generic smooth functions is indicated. Possible applications are sketched.
We consider locally o-minimal structures possessing tame topological properties shared by models of DCTC and uniformly locally o-minimal expansions of the second kind of densely linearly ordered abelian groups. We derive basic properties of…
In several recent papers some concepts of convex analysis were extended to discrete sets. This paper is one more step in this direction. It is well known that a local minimum of a convex function is always its global minimum. We study some…
Recent work of Pickett has given a construction of self-dual normal bases for extensions of finite fields, whenever they exist. In this article we present these results in an explicit and constructive manner and apply them, through computer…
In this article we introduce a definition of topological minimal sets, which is a generalization of that of Mumford-Shah-minimal sets. We prove some general properties as well as two existence theorems for topological minimal sets. As an…
We consider polygonal tilings of certain regions and use these to give intuitive definitions of tiling-based perimeter and area. We apply these definitions to rhombic tilings of Elnitsky polygons, computing sharp bounds and average values…
In this work we review and derive some elementary properties of the discrete renewal sequences based on a positive, finite and integer-valued random variable. Our results consider these sequences as dependent on the probability masses of…
In this paper, we give the definition of {\em weakly locally finite} division rings and we show that the class of these rings strictly contains the class of locally finite division rings. Further, we study multiplicative subgroups in these…
Within the framework of finite element systems, we show how spaces of differential forms may be constructed, in such a way that they are equipped with commuting interpolators and contain prescribed functions, and are minimal under these…
Ring epimorphisms often induce silting modules and cosilting modules, termed minimal silting or minimal cosilting. The aim of this paper is twofold. Firstly, we determine the minimal tilting and minimal cotilting modules over a tame…
The paper intends to apply the properties of Pr\"ufer extensions, investigated in the Knebusch-Zhang book, to ring extensions $R\subseteq S$. The integral closure $\overline R$ of $R$ in $S$ is shown to be the intersection of all $T\in…
We prove some basic properties of quasinearly subharmonic functions and quasinearly subharmonic functions in the narrow sense.