Identities in algebras with involution

Normed algebras with involution

We show that most of the theory of Hermitian Banach algebras can be proved for normed ∗-algebras without the assumption of completeness. The condition r(x) ≤ p(x) for all x (where p(x) = r(x∗x)1/2 is the Pták function), which is essential in the theory of Hermitian Banach algebras, is replaced for normed ∗-algebras by the condition r(x + y) ≤ p(x) + p(y) for all x, y. In case of Banach ∗-algebr...

Ultra and Involution Ideals in $BCK$-algebras

In this paper, we define the notions of ultra and involution ideals in $BCK$-algebras. Then we get the relation among them and other ideals as (positive) implicative, associative, commutative and prime ideals. Specially, we show that in a bounded implicative $BCK$-algebra, any involution ideal is a positive implicative ideal and in a bounded positive implicative lower $BCK$-semilattice, the not...

Generic Algebras with Involution Of

2-local Mappings on Algebras with Involution

We investigate 2-local ∗-automorphisms, 2-local ∗-antiautomorphisms, and 2-local Jordan ∗-derivations on certain algebras with involution.

ALGEBRAIC ALGEBRAS WITH INVOLUTION susan montgomery

The following theorem is proved: Let R be an algebra with involution over an uncountable field F. Then if the symmetric elements of R are algebraic, R is algebraic. In this paper we consider the following question: "Let R be an algebra with involution over a field F, and assume that the symmetric elements S of R are algebraic over F. Is R algebraic over FT* Previous results related to this ques...