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A finite presentation of Jordan algebras

Instituto de Matematica e Estatistica, Universidade de São Paulo, Caisa Postal 66 281, CEP 05315-970, São Paulo, Brazil

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Department of Mathematics, University of California at San Diego, 9500 Gilman Drive, La Jolla, California 92093-0112, USA

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https://doi.org/10.1142/S0218196718400155Cited by:2 (Source: Crossref)

This article is part of the issue:

Special Issue on Groups, Algebras and Identities in Honor of Professor Boris Plotkin's 90th Birthday; Guest Editor: E. Plotkin

Abstract

Let $R$ $R$ be an associative algebra. Let $* : R \to R$ $* : R \to R$ be an involution. We study the following question: when are the Jordan algebras $R^{(+)}$ $R^{(+)}$ and $H (R, *) = {a \in R | a^{*} = a}$ $H (R, *) = {a \in R | a^{*} = a}$ finitely presented?

Communicated by E. Plotkin

To Boris Isaakovich Plotkin with admiration

Keywords:

AMSC: 17C10, 17C50

References

1. P. M. Cohn, On homomorphic images of special Jordan algebras, Canadian J. Math. 6 (1954) 253–264, MR 0060496. Crossref, Web of Science, Google Scholar
2. I. N. Herstein, Rings with Involution, Chicago Lectures in Mathematics (The University of Chicago Press, Chicago, 1976), MR 0442017. Google Scholar
3. N. Jacobson, Structure and Representations of Jordan Algebras, American Mathematical Society Colloquium Publications, Vol. XXXIX (American Mathematical Society, Providence, R.I., 1968), MR 0251099. Crossref, Google Scholar
4. A. I. Shirshov, On special J-rings, Mat. Sb. (N.S) 38(80) (1956) 149166, MR 0075936. Google Scholar
5. E. I. Zelmanov, Prime Jordan algebras. II, Sibirsk. Mat. Zh. 24(1) (1983) 89–104, MR 688595. Web of Science, Google Scholar
6. K. A. Zhevlakov, Solvability and nilpotence of Jordan rings, Algebra i Logika Sem 5 (1966) 37–58, MR 0207786. Google Scholar
7. K. A. Zhevlakov, A. M. Slinko, I. P. Shestakov and A. I. Shirshov, Rings that are Nearly Associative, Pure and Applied Mathematics, Vol. 104 (Academic Press, Inc. New York, 1982), translated from the Russian by Harry F. Smith, MR 668355. Google Scholar