–a notion of amenability for topological semigroups is introduced. a topological semigroup s iscalled johnson amenable if for every banach s -bimodule e , every bounded crossed homomorphism froms to e* is principal. in this paper it is shown that a discrete semigroup s is johnson amenable if and only if1(s) is an amenable banach algebra. also, we show that if a topological semigroup s is johns...

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.

A basic problem in the theory of Lie algebra extensions concerns a given homomorphism x of a Lie algebra L into the Lie algebra of outer derivations of a Lie algebra B . In analogy with the theory of group extensions, Mori and HochschiId developed the concept of an obstruction to x being the homomorphism defined by some Lie algebra extension of B by L . This note considers an alternative approa...

In the group of (continuous) Jordan automorphisms, with the uniform topology, on a semisimple Banach algebra, we show that the connected component of the identity consists of automorphisms. P. Civin and B. Yood have shown that a Jordan homomorphism (that is, a homomorphism that preserves the product xoy = | (xy+yx)) from a Banach algebra onto a semisimple Banach algebra is continuous provided t...

Let $f : A rightarrow B$ be a ring homomorphism and $J$ an ideal of $B$. In this paper, we give a necessary and sufficient condition for the amalgamated algebra along an ideal $Abowtie^fJ$ to be $J$-Noetherian. Then we give a characterization for pseudo-irreducible ideals of $Abowtie^fJ$, in special cases.

In this paper, applying the concept of generalized A-valued norm on a right $H^*$-module and also the notion of ϕ-homomorphism of Finsler modules over $C^*$-algebras we first improve the definition of the Finsler module over $H^*$-algebra and then define ϕ-morphism of Finsler modules over $H^*$-algebras. Finally we present some results concerning these new ones.

In this paper we introduce a notion of vertex Lie algebra U , in a way a “half” of vertex algebra structure sufficient to construct the corresponding local Lie algebra L(U) and a vertex algebra V(U). We show that we may consider U as a subset U ⊂ V(U) which generates V(U) and that the vertex Lie algebra structure on U is induced by the vertex algebra structure on V(U). Moreover, for any vertex ...

To any finite group Γ ⊂ Sp(V ) of automorphisms of a symplectic vector space V we associate a new multi-parameter deformation, Hκ, of the algebra C[V ]#Γ, smash product of Γ with the polynomial algebra on V . The parameter κ runs over points of CP , where r =number of conjugacy classes of symplectic reflections in Γ. The algebra Hκ, called a symplectic reflection algebra, is expected to be rela...

In this paper, we apply the concept of fuzzy set to ideals and closed ideals in B-algebras. The notion of a fuzzy closed ideal of a B-algebra is introduced, and some related properties are investigated. Also, the product of fuzzy B-algebra is investigated. Keywords—B-algebras, fuzzy sets, fuzzy ideals, homomorphism, fuzzy closed ideals, homomorphism, equivalence relation, level cut, product of ...