Related papers: Ideal Extensions and Directly Infinite Algebras

We prove that if two homomorphisms from O_{\infty} to a purely infinite simple C*-algebra have the same class in KK-theory, and if either both are unital or both are nonunital, then they are approximately unitarily equivalent. It follows…

Let $A$ be a separable amenable $C^*$-algebra and $B$ a non-unital and $\sigma$-unital simple $C^*$-algebra with continuous scale ($B$ need not be stable). We classify, up to unitary equivalence, all essential extensions of the form $0…

This article explores some simple examples of L-infinity algebras and the construction of miniversal deformations of these structures. Among other things, it is shown that there are two families of nonequivalent L-infinity structures on a…

Let k be a field of characteristic zero. We consider graded subalgebras A of k[x_1,...,x_m]/(x_1^2,...,x_m^2) generated by d linearly independant linear forms. Representations of matroids over k provide a natural description of the…

The class of AD algebras of real rank zero is classified by an exact sequence of K-groups with coefficients, equipped with certain order structures. Such a sequence is always split, and one may ask why, then, the middle group is relevant…

In earlier work, it was established that for any finite field k, the free associative k-algebra on one generator x, denoted by k[x]_0, had infinitely many maximal T-spaces, but exactly two maximal $ideals (each of which is a maximal…

Let M be a maximal subalgebra of the Lie algebra L. A subalgebra C of L is said to be a completion for M if C is not contained in M but every proper subalgebra of C that is an ideal of L is contained in M. The set I(M) of all completions of…

The note presents a further study of the class of Cuntz--Krieger type algebras. A necessary and sufficient condition is identified that ensures that the algebra is purely infinite, the ideal structure is studied, % and applied to semigraph…

In this paper we define almost gentle algebras. They are monomial special multiserial algebras generalizing gentle algebras. We show that the trivial extension of an almost gentle algebra by its minimal injective co-generator is a symmetric…

An algebraically expandable (AE) class is a class of algebraic structures axiomatizable by sentences of the form $\forall \exists! \land p = q$. For a logic $L$ algebraized by a quasivariety $\mathcal{Q}$ we show that the AE-subclasses of…

This paper investigates the application of the theoretical algebraic notion of a separable ring extension, in the realm of cyclic convolutional codes or, more generally, ideal codes. We work under very mild conditions, that cover all…

In this paper, we exhibit two unital, separable, nuclear ${\rm C}^*$-algebras of stable rank one and real rank zero with the same ordered scaled total K-theory, but they are not isomorphic with each other, which forms a counterexample to…

We introduce the Hochschild extensions of dg algebras, which are $A_\infty$-algebras. We show that all exact Hochschild extensions are symmetric Hochschild extensions, more precisely, every exact Hochschild extension of a finite dimensional…

Criteria are obtained for a filter F of subsets of a set I to be an intersection of finitely many ultrafilters, respectively, finitely many \kappa-complete ultrafilters for a given uncountable cardinal \kappa. From these, general results…

The paper concerns perfect diassociative algebras and their implications to the theory of central extensions. It is first established that perfect diassociative algebras have strong ties with universal central extensions. Then, using a…

Nilpotent Leibniz algebras with isomorphic maximal subalgebras are considered. The algebras are classified for coclass zero, one, and two. The results are field dependent.

We study the differential identities of the algebra $M_k(F)$ of $k\times k$ matrices over a field $F$ of characteristic zero when its full Lie algebra of derivations, $L=\mbox{Der}(M_k(F))$, acts on it. We determine a set of 2 generators of…

The main aim of this paper is to characterize ideals I in the power series ring R=K[[x1,...,xs]] that are finitely determined up to contact equivalence by proving that this is the case if and only if I is an isolated complete intersection…

We consider the intersection $\mathfrak{M}(A)$ of all maximal ideals of an evolution algebra $A$ and study the structure of the quotient $A/\M(A)$. In a previous work, maximal ideals have been related to hereditary subsets of a graph…

We prove that if two nonzero homomorphisms from the Cuntz algebra O_infinity to a purely infinite simple C*-algebra have the same class in KK-theory, and if either both are unital or both are nonunital, then they are approximately unitarily…