In this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf F}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf F}$ of positive characteristic $p$. Moreover, we find a one-to-one correspondence between $p$-semiline...

Bernstein algebras were introduced by Holgate [6] as an algebraic formulation of the problem of classifying the stationary evolution operators in genetics (see [8]). Since then, many authors have contributed to the study of these algebras, and there is a fairly extensive bibliography on the subject. Known results include classification theorems for sorre types of Bernstein algebras (for instanc...

In fact, if X is any vector space on which the primitive Banach algebra A acts faithfully and irreducibly, then X can be converted in a Banach space in such a way that the requirements in Theorem 0 are satisfied and even the inclusion A9BL(X ) is contractive. Roughly speaking, the aim of this paper is to prove the appropriate Jordan variant of Theorem 0. The notion of primitiveness for Jordan a...

If a vertex operator algebra V = ⊕n=0Vn satisfies dimV0 = 1, V1 = 0, then V2 has a commutative (nonassociative) algebra structure called Griess algebra. One of the typical examples of commutative (nonassociative) algebras is a Jordan algebra. For example, the set Symd(C) of symmetric matrices of degree d becomes a Jordan algebra. On the other hand, in the theory of vertex operator algebras, cen...

Let n ∈ N − {1}, and let A be a Banach algebra. An additive map D : A → A is called n-Jordan derivation if D(a) = D(a)a + aD(a)a + ...+ aD(a)a+ aD(a), for all a ∈ A. Using fixed point methods, we investigate the stability of n–Jordan derivations (n–Jordan ∗−derivations) on Banach algebras (C∗−algebras). Also we show that to each approximate ∗−Jordan derivation f in a C∗− algebra there correspon...

and x y denotes the product x ‘3~ = my + y.2’. In Section 1 we show that a noncommutative Jordan algebra of characteristic # 2 must satisfy (1). Since power-associative algebras satisfying (1) need not be flexible [5] it follows that the class of power-associative algebras satisfying (1) is strictly larger than the class of noncommutative Jordan algebras. In Section 2 we obtain a structure theo...

Using fixed pointmethods, we investigate approximately higher ternary Jordan derivations in Banach ternaty algebras via the Cauchy functional equation$$f(lambda_{1}x+lambda_{2}y+lambda_3z)=lambda_1f(x)+lambda_2f(y)+lambda_3f(z)~.$$

The purpose of this paper is to fill a gap in Albert's structure theory' of abstract Jordan algebras of any characteristic $2, by proving the following: THEOREM A. Let 21 be a finite-dimensional Jordan algebra over a field (. Assume (1) that 21 has an identity element u and (2) that every element of 21 has the form au + z, where a e (D and z is nilpotent. Then 21 = 4u + A3, where Z is a nil sub...

We prove that Jordan elementary surjective maps on rings are automatically additive. Elementary operators were originally introduced by Brešar and Šerml ([1]). In the last decade, elementary maps on operator algebras as well as on rings attracted more and more attentions. It is very interesting that elementary maps and Jordan elementary maps on some algebras and rings are automatically additive...

in this paper, we introduce $p$-semilinear transformations for linear algebras over a field ${bf f}$ of positive characteristic $p$, discuss initially the elementary properties of $p$-semilinear transformations, make use of it to give some characterizations of linear algebras over a field ${bf f}$ of positive characteristic $p$. moreover, we find a one-to-one correspondence between $p$-semiline...