Related papers: Complete intersection vanishing ideals on sets of …
In this paper we give conditions on a homogeneous polynomial for which the associated graded Artin algebra is a complete intersection.
We study the concept of universal sets from the additive--combinatorial point of view. Among other results we obtain some applications of this type of uniformity to sets avoiding solutions to linear equations, and get an optimal upper bound…
We show that the pure mapping class group is uniformly perfect for a certain class of infinite type surfaces with noncompact boundary components. We then combine this result with recent work in the remaining cases to give a complete…
We classify plethories over fields of characteristic zero, thus answering a question of Borger-Wieland and Bergman-Hausknecht. All plethories over characteristic zero fields are linear, in the sense that they are free plethories on a…
We prove rigidity type results on the vanishing of stable (co)homology for modules of finite complete intersection dimension, results which generalize and improve upon known results. We also introduce a notion of pre-rigidity, which…
Let $M$ be a finitely generated module over a local complete intersection $R$ of characteristic $p>0$. The property that $M$ has finite projective dimension can be characterized by the vanishing of $\ext_R^i({}^{f^n} R,M)$ for some $i>0$…
We present and study some transfinite versions of (almost isometric) ideals in Banach spaces. As these notions are closely related with Lindenstrauss and Gurari\u{\i} spaces respectively, we will present a similar characterization for…
In this paper, we prove weak elimination of imaginaries for perfect bounded pseudo-algebraically closed fields equipped with finitely many independent valuations. Our approach combines an extension result for types to invariant types with…
We give a positive answer to the Huneke-Wiegand Conjecture for monomial ideals over free numerical semigroup rings, and for two generated monomial ideals over complete intersection numerical semigroup rings.
We survey the theory of totally symmetric sets, with applications to homomorphisms of symmetric groups, braid groups, linear groups, and mapping class groups.
We survey recent developments on mapping class groups of surfaces of infinite topological type.
We compute the list of all minimal 2-infinite diagrams, which are cluster algebraic analogues of extended Dynkin graphs.
We describe the canonical correspondence between set of all finite metric spaces and set of special symmetric convex polytopes, and formulate the problem about classification of the metric spaces in terms of combinatorial structure of those…
This paper studies two topics concerning on the orthogonal complement of one dimensional subspace with respect to a given quadratic form on a vector space over a number field. One is to determine the invariants for the isomorphism class of…
The Hilbert polynomial of a homogeneous complete intersection is determined by the degrees of the generators of the defining ideal. The degrees of the generators are not, in general, determined by the Hilbert polynomial -- but sometimes…
We present a clear and practical way to characterize the parabolicity of a complete immersed surface that is invariant with respect to a Killing vector field of the ambient space.
We study the set of algebraic objects known as vanishing polynomials (the set of polynomials that annihilate all elements of a ring) over general commutative rings with identity. These objects are of special interest due to their close…
In this paper we shall consider the Lie algebra of column-finite infinite matrices indexed by positive integers $\mathbb{N}$, describe the lattice of its ideals for arbitrary field $K$ and study its derivations over any commutative, unital…
In order to simultaneously generalize matrix rings and group graded crossed products, we introduce category crossed products. For such algebras we describe the center and the commutant of the coefficient ring. We also investigate the…
We survey some aspects of the perfect matching problem in hypergraphs, with particular emphasis on structural characterisation of the existence problem in dense hypergraphs and the existence of designs.