Related papers: On saturated uniformly A-convex algebras

Equational Artinian algebras were introduced in our previous work: {\em Equational conditions in universal algebraic geometry, to appear in Algebra and Logic, 2015}. In this note, we define the notion of {\em radical topology with respect…

F. Wehrung has asked: Given a family $\mathcal{C}$ of subsets of a set $\Omega$, under what conditions will there exist a total ordering on $\Omega$ under which every member of $\mathcal{C}$ is convex? <p> Note that if $A$ and $B$ are…

Universal algebraic geometry is generalised from solutions of equations in a single algebra to the study of $\varphi$- or $K$-spectra, akin to the prime spectrum of a ring. We explore their basic properties and constructions, give a…

A novel algebra underlying integrable systems is shown to generate and unify a large class of quantum integrable models with given $R$-matrix, through reductions of an ancestor Lax operator and its different realizations. Along with known…

We introduce a new class of algebras, which we call cluster-tilted. They are by definition the endomorphism algebras of tilting objects in a cluster category. We show that their representation theory is very close to the representation…

We study associative multiplications in semi-simple associative algebras over C compatible with the usual one or, in other words, linear deformations of semi-simple associative algebras over C. It turns out that these deformations are in…

A topological space $X$ is defined to have an $\omega^\omega$-base if at each point $x\in X$ the space $X$ has a neighborhood base $(U_\alpha[x])_{\alpha\in\omega^\omega}$ such that $U_\beta[x]\subset U_\alpha[x]$ for all $\alpha\le\beta$…

We describe $\sigma$-matching, interchangeable and, as a consequence, totally compatible products on some classes of associative algebras, including unital algebras, the semigroup algebras of rectangular bands, algebras with enough…

In this paper we denote a type of affine homogeneous real hypersurface of $\mathbb{C}^3$ and present a classification of homogeneous surfaces of the type (1/2,0). The result was obtained by reducing the classification problem mentioned…

We show that any regular pseudocomplemented Kleene algebra defined on an algebraic lattice is isomorphic to a rough set Kleene algebra determined by a tolerance induced by an irredundant covering.

The notion of a derived A-infinity algebra, considered by Sagave, is a generalization of the classical notion of A-infinity algebra, relevant to the case where one works over a commutative ring rather than a field. We initiate a study of…

In this article, we classify (non-compact) $3$-manifolds with uniformly positive scalar curvature. Precisely, we show that an oriented $3$-manifold has a complete metric with uniformly positive scalar curvature if and only if it is…

Let $C_b(X)$ be the C*-algebra of bounded continuous functions on some non-compact, but locally compact Hausdorff space $X$. Moreover, let $A_0$ be some ideal and $A_1$ be some unital C*-subalgebra of $C_b(X)$. For $A_0$ and $A_1$ having…

We derive an upper bound on the size of a ball such that the image of the ball under quadratic map is strongly convex and smooth. Our result is the best possible improvement of the analogous result by Polyak in the case of quadratic map. We…

We define a broad class of crossed product C*-algebras of the form C(G)xG, where G is a discrete countable amenable residually finite group, and G is a profinite completion of G. We show that they are unital separable simple nuclear…

We introduce the notion of bounded quasi-inversion closed semiprime f-algebras and we prove that, if A is such an algebra, then any intermediate algebra in A is an order ideal of A. This extends a recent result by Dominguez who has dealt…

A convex polygon is defined as a sequence (V_0,...,V_{n-1}) of points on a plane such that the union of the edges [V_0,V_1],..., [V_{n-2},V_{n-1}], [V_{n-1},V_0] coincides with the boundary of the convex hull of the set of vertices…

This article is an expository account of the theory of twisted commutative algebras, which simply put, can be thought of as a theory for handling commutative algebras with large groups of linear symmetries. Examples include the coordinate…

Uniform Lie algebras are combinatorially defined two-step nilpotent Lie algebras which can be used to define Einstein solvmanifolds. These Einstein spaces often have nontrivial isotropy groups. We derive basic properties of uniform Lie…

Given a C$^*$-correspondence $X$, we give necessary and sufficient conditions for the tensor algebra $\mathcal T_X^+$ to be hyperrigid. In the case where $X$ is coming from a topological graph we obtain a complete characterization.