On multiplication algebras

Author:
David R. Finston

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

MSC:
Primary 17A99; Secondary 16A99

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

MathSciNet review:
816327

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

Article copyright:
© Copyright 1986
American Mathematical Society