A (variable-length) code is a free subset of a free monoid; more formally, it is the basis of some free submonoid. The theory of these codes (not to be confused with error-detecting codes) was first developed by M.P. Schiitzenberger. A major problem in this theory is to factorize codes, that is, considering the characteristic formal power series of a code (in the noncommutat ive formal power se...

In this paper we study Schur-Weyl duality between the symplectic group and Brauer’s centralizer algebra over an arbitrary infinite field K. We show that the natural homomorphism from the Brauer’s centralizer algebra Bn(−2m) to the endomorphism algebra of tensor space (K) as a module over the symplectic similitude group GSp2m(K) (or equivalently, as a module over the symplectic group Sp2m(K)) is...

Let A,B be two unital C∗−algebras. We prove that every almost unital almost linear mapping h : A −→ B which satisfies h(3uy + 3yu) = h(3u)h(y) + h(y)h(3u) for all u ∈ U(A), all y ∈ A, and all n = 0, 1, 2, ..., is a Jordan homomorphism. Also, for a unital C∗−algebra A of real rank zero, every almost unital almost linear continuous mapping h : A −→ B is a Jordan homomorphism when h(3uy + 3yu) = h...

Mathieu and Ruddy proved that if be a unital spectral isometry from a unital C*-algebra Aonto a unital type I C*-algebra B whose primitive ideal space is Hausdorff and totallydisconnected, then is Jordan isomorphism. The aim of this note is to show that if be asurjective spectrum preserving additive map, then is a Jordan isomorphism without the extraassumption totally disconnected.

Introduction. It has been shown in a previous paper [3]1 that every algebra A with radical R, such that A/R is separable, is a homomorphic image of a certain maximal algebra which is determined to within an isomorphism by A/R, the A/R-modu\e (two-sided) R/R1, and the index of nilpotency of R. Furthermore, some indication was given of how the structure of maximal algebras can be determined in si...

In this paper we study the concept of ph-biatness ofa Banach algebra A, where ph is a continuous homomorphism on A.We prove that if ph is a continuous epimorphism on A and A hasa bounded approximate identity and A is ph- biat, then A is ph-amenable. In the case where ph is an isomorphism on A we showthat the ph- amenability of A implies its ph-biatness.

in this paper, we consider a class of connected oriented (with respect to z/p) closed g-manifolds with a non-empty finite fixed point set, each of which is g-equivariantly formal, where g = z/p and p is an odd prime. using localization theorem and equivariant index, we give an explicit description of the mod p equivariant cohomology ring of such a g-manifold in terms of algebra. this makes it p...

Every continuous map X → S defines, by composition, a homomorphism between the corresponding algebras of real-valued continuous functions C(S) → C(X). This paper deals with algebraic properties of the homomorphism C(S)→ C(X) in relation to topological properties of the map X → S. The main result of the paper states that a continuous map X → S between topological manifolds is a finite (branched)...

Contents 1. Introduction 1 2. Carlitz-Fermat quotients 2 3. Non-vanishing of Carlitz-Fermat quotients modulo primes 4 1. Introduction. Let q = p s , where p is a prime and s is a positive integer. Let F q be the finite field of q elements, and set A = F q [T ] and k = F q (T). Let τ be the mapping defined by τ (x) = x q , and let kτ denote the twisted polynomial ring. Let C : A → kτ (a → C a) b...