Related papers: On equationally Noetherian predicate structures
It is shown that a quiver is left noetherian if and only if the category of quiver representations in any locally noetherian abelian category is again locally noetherian. Here, locally noetherian means that any object is the directed union…
Let $G$ be a group with neutral element $e$ and let $S=\bigoplus_{g \in G}S_g$ be a $G$-graded ring. A necessary condition for $S$ to be noetherian is that the principal component $S_e$ is noetherian. The following partial converse is…
In this paper we prove an algebraic criterion which characterizes singular quasi-bi-hamiltonian structures constructed on the lines of a general, simple, new formal procedure proposed by the authors. This procedure shows that for the…
In this paper we prove an algebraic criterion which characterizes singular quasi-bi-hamiltonian structures constructed on the lines of a general, simple, new formal procedure proposed by the authors. This procedure shows that for the…
We prove coherence of relatively quasi-free algebras over noetherian rings. Chase criterion for coherence is used.
We show uniqueness up to sign of positive, orthogonal almost-Kaehler structures on any non-scalar flat Kaehler-Einstein surface.
This paper obtains a completeness result for inequational reasoning with applicative terms without variables in a setting where the intended semantic models are the full structures, the full type hierarchies over preorders for the base…
If $(X, \le_X)$ is a partially ordered set satisfying certain necessary conditions for $X$ to be order-isomorphic to the spectrum of a Noetherian domain of dimension two, we describe a new poset $(\text{str } X, \le_{\text{str } X})$ that…
In this paper, a computably definable predicate is defined and characterized. Then, it is proved that every separable infinite-dimensional Hilbert structure in an effectively presented language is computable. Moreover, every definable…
We give a criterion for a real divisor to be rational and semiample.
We give a criterion in terms of period matrices for an arbitrary polarized abelian variety to be non-simple. Several examples are worked out.
The goal of this expository article, based on a lecture I gave at the 2016 ICRA, is to explain some recent applications of "categorical symmetries" in topology and algebraic geometry with an eye toward twisted commutative algebras as a…
We obtain sufficient conditions ensuring the topological equivalence of two perturbed difference linear systems whose linear part has a property of generalized exponential dichotomy. When the exponential dichotomy is verified, we obtain a…
We investigate a hierarchy of arithmetical structures obtained by a transfinite addition of a canonic universal predicate, where the canonic universal predicate for M is defined as a minimum universal predicate for M in terms of…
We give sharp criteria for when a reductive group scheme satisfies Tannakian reconstruction. When the base scheme is Noetherian, we explicitly identify its Tannaka group scheme.
This article discusses a criterion to determine residual variables of an $\mathbb{A}^2$-fibration over a Noetherian domain containing $\mathbb{Q}$.
In this article, we develop a technique to "split" certain types of partially ordered sets into simpler ones and use that technique to give a partial answer to a conjecture by R. Wiegand and S. Wiegand on the structure of semi-local,…
Let K be a field of characteristic zero. Motivated by the conjecture that an enveloping algebra U(g) is Noetherian only if g is finite dimensional, we define the notion of weakly Noetherian Lie algebras. The main result, Theorem A, states…
Using the notion of existentially closed structures, we obtain embedding theorems for groups and Lie algebras. We also prove the existence of some groups and Lie algebras with prescribed properties.
In this paper we develop a Grobner bases theory for ideals of partial difference polynomials with constant or non-constant coefficients. In particular, we introduce a criterion providing the finiteness of such bases when a difference ideal…