Algebras defined by homomorphisms

algebras defined by homomorphisms

let $mathcal{r}$ be a  commutative ring with identity, let $a$ and $b$ be two $mathcal{r}$-algebras and $varphi:blongrightarrow a$ be an $mathcal{r}$-additive algebra homomorphism. we introduce a new algebra $atimes_varphi b$, and give some basic properties of this algebra. generalized $2$-cocycle derivations on $atimes_varphi b$ are studied. accordingly, $atimes_varphi b$ is considered from th...

Module homomorphisms from Frechet algebras

We first study some properties‎ ‎of $A$-module homomorphisms $theta:Xrightarrow Y$‎, ‎where $X$‎ ‎and $Y$ are Fréchet $A$-modules and $A$ is a unital‎ ‎Fréchet algebra‎. ‎Then we show that if there exists a‎ ‎continued bisection of the identity for $A$‎, ‎then $theta$ is‎ ‎automatically continuous under certain condition on $X$‎. ‎In‎ ‎particular‎, ‎every homomorphism from $A$ into certain‎ ‎Fr...

Fuzzy homomorphisms of algebras

In this paper we consider fuzzy relations compatible with algebraic operations, which are called fuzzy relational morphisms. In particular, we aim our attention to those fuzzy relational morphisms which are uniform fuzzy relations, called uniform fuzzy relational morphisms, and those which are partially uniform F -functions, called fuzzy homomorphisms. Both uniform fuzzy relations and partially...

MODULE HOMOMORPHISMS ASSOCIATED WITH HYPERGROUP ALGEBRAS

Let X be a hypergroup. In this paper, we study the homomorphisms on certain subspaces of L(X)* which are weak*-weak* continuous.

Triple Homomorphisms of C*-algebras

In this note, we will discuss what kind of operators between C*-algebras preserves Jordan triple products {a, b, c} = (abc + cba)/2. These include especially isometries and disjointness preserving operators.

Automatic Continuity of Homomorphisms Between Banach algebras and Frechet algebras