In this paper we introduce the notions of fuzzy transposition hypergroupsand fuzzy regular relations and investigate their basic properties.We also study fuzzy quotient hypergroups of a fuzzy transposition hypergroup.

Let R be a ring, CR and ′CR be the set of regular and left regular elements of R (CR ⊆ ′CR). Goldie’s Theorem is a semisimplicity criterion for the classical left quotient ring Ql,cl(R) := C −1 R R. Semisimplicity criteria are given for the classical left regular left quotient ring ′Ql,cl(R) := ′C −1 R R. As a corollary, two new semisimplicity criteria for Ql,cl(R) are obtained (in the spirit o...

In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach algebras. Then we study their Arens regularity as well as their topological centers . In this paper we first introduce a new multiplication on triangular Banach ...

For a compact space X we consider extending endomorphisms of the algebra C(X) to be endomorphisms of Arens-Hoffman and Cole extensions of C(X). Given a non-linear, monic polynomial p ∈ C(X)[t], with C(X)[t]/pC(X)[t] semi-simple, we show that if an endomorphism of C(X) extends to the Arens-Hoffman extension with respect to p then it also extends to the simple Cole extension with respect to p. We...

Throughout this paper, G denotes a simple and simply connected algebraic group over C of rank r and H is a Cartan subgroup, with Lie algebras g = LieG and h = LieH. Let R be the root system of the pair (G,H), W the Weyl group, and Λ ⊆ h the coroot lattice. Fix once and for all a positive Weyl chamber, i.e. a set of simple roots ∆. The geometric invariant theory quotient of g by the adjoint acti...

We survey recent results concerning the complexity of regular languages represented by their minimal deterministic finite automata. In addition to the quotient complexity of the language – which is the number of its (left) quotients, and is the same as its state complexity – we also consider the size of its syntactic semigroup and the quotient complexity of its atoms – basic components of every...