On multiplication algebras

Finston, David R.

doi:10.1090/S0002-9947-1986-0816327-2

On multiplication algebras
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by David R. Finston

Trans. Amer. Math. Soc. 293 (1986), 807-818

DOI: https://doi.org/10.1090/S0002-9947-1986-0816327-2

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Abstract:

The basic properties of multiplication algebras of nonassociative algebras over rings are introduced, including a discussion of multiplication algebras of tensor products of algebras. A characterization of semisimple artinian multiplication algebras is given along with a discussion of the nature of the simple factors of a multiplication algebra modulo its Jacobson radical. A criterion distinguishing the multiplication algebras of certain associative algebras is proved. Examples are included to illustrate certain proved results.

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