An identity in prime superalgebras

In this paper we investigate the functional identity in a prime associative superalgebras. We prove the following result. Suppose that there exists a nonzero additive mapping f = f 0 + f 1 , on a prime associative superalgebra with char(R) ≠ 2, satisfying the relation [f (x), y 2 ] = 0 for all x, y...

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Published inQuaestiones mathematicae Vol. 42; no. 4; pp. 451 - 464
Main Authors Fošner, Ajda, Fošner, Maja, Marcen, Benjamin
Format Journal Article
LanguageEnglish
Published Grahamstown Taylor & Francis 21.04.2019
Taylor & Francis Ltd
Subjects
extended centroid
Mapping
prime superalgebra
semiprime superalgebra
Superalgebra
supercommutator
superderivation
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Summary:In this paper we investigate the functional identity in a prime associative superalgebras. We prove the following result. Suppose that there exists a nonzero additive mapping f = f 0 + f 1 , on a prime associative superalgebra with char(R) ≠ 2, satisfying the relation [f (x), y 2 ] = 0 for all x, y ∈ ℋ( ). If is prime algebra then [f ( ), ] = 0 or [ , ] = 0. 0 is prime algebra then [f ( ), ] = 0 and [ , 0 ] = 0 or A is trivial. More- over, if C 1 = 0 then f 0 ( 1 ) = 0 and f 1 ( 0 ) = 0.
ISSN:1607-3606
1727-933X
DOI:10.2989/16073606.2018.1458756