Algebra extensions A ⊆ B where A is a left B-module such that the Baction extends the multiplication in A are ubiquitous. We encounter examples of such extensions in the study of group actions, group gradings or more general Hopf actions as well as in the study of the bimodule structure of an algebra. In this paper we are extending R.Wisbauer’s method of constructing the central closure of a se...

The aim of this paper is to introduce the notion of anti fuzzy (prime) deductive system in BL-algebra and to investigate their properties. It is shown that the set of all deductive systems (with the empty set) of a BL-algebra X is equipotent to a quotient of the set of all anti fuzzy deductive systems of X. The anti fuzzy prime deductive system theorem of BL-algebras is also proved. Anti Fuzzy ...

We construct Boolean-valued term models and describe their universal properties. The underlying set of these models consists of the terms of the underlying language, while formulae are interpreted in the Lindenbaum-Tarski algebra of open formulae. Subspaces of the Stone space of the Lindenbaum-Tarski algebra of open formulae are shown to be homeomorphic to spaces of enumerated models models equ...

To each integral domain R with finite quotients we associate a purely infinite simple C*-algebra in a very natural way. Its stabilization can be identified with the crossed product of the algebra of continuous functions on the “finite adele space” corresponding to R by the action of the ax+ b-group over the quotient field Q(R). We study the relationship to generalized Bost-Connes systems and de...

The “spectral picture” of a bounded operator on a Banach space consists of its essential spectrum together with a mapping from its holes to the group of integers, obtained by taking the Fredholm index. In this note we abstract this from the Calkin algebra to a general Banach algebra, replacing the integers with the quotient of the group of invertibles by its connected component of the identity.

In this paper we introduce some types of filters in a BL algebra A, and we state and prove some theorems which determine the relationship between these notions and other filters of a BL algebra, and by some examples we show that these notions are different. Also we consider some relations between these filters and quotient algebras that are constructed via these filters. Mathematics Subject Cla...

Let k be an uncountable algebraically closed field and let A be a countably generated left Noetherian k-algebra. Then we show that A⊗k K is left Noetherian for any field extension K of k. We conclude that all subfields of the quotient division algebra of a countably generated left Noetherian domain over k are finitely generated extensions of k. We give examples which show that A⊗k K need not re...

Abstract. Newman, Schneider and Shalev defined the entropy of a graded associative algebra A as H(A) = lim sup n→∞ n √ an, where an is the vector space dimension of the n’th homogeneous component. When A is the homogeneous quotient of a finitely generated free associative algebra, they showed that H(A) ≤ √ a2. Using some results of Friedland on the maximal spectral radius of (0, 1)-matrices wit...

We show that the weighted fusion category algebra of the principal 2-block b0 of GL2(q) is the quotient of the q-Schur algebra S2(q) by its socle, for q an odd prime power. As a consequence, we get a canonical bijection between the set of isomorphism classes of simple kGL2(q)b0-modules and the set of conjugacy classes of b0-weights in this case.

We study the Brauer–Schur–Weyl duality between the quotient Bn(−2m)/B (f) n of the Brauer algebra Bn(−2m) and the symplectic group Sp(V ) on the space HT ⊗f n of partially harmonic tensors of valence f in V , where B (f) n is the two-sided ideal generated by e1e3 · · · e2f−1 and 1 ≤ f ≤ [n/2]. We prove that the dimensions of HT ⊗f n and the endomorphism algebra EndKSp(V ) “