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Free Akivis Algebras, Primitive Elements, and Hyperalgebras

✍ Scribed by Ivan P. Shestakov; Ualbai U. Umirbaev

Publisher: Elsevier Science
Year: 2002
Tongue: English
Weight: 129 KB
Volume: 250
Category: Article
ISSN: 0021-8693
DOI: 10.1006/jabr.2001.9123

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✦ Synopsis

Free Akivis algebras and primitive elements in their universal enveloping algebras are investigated. It is proved that subalgebras of free Akivis algebras are free and that finitely generated subalgebras are finitely residual. Decidability of the word problem for the variety of Akivis algebras is also proved.

The conjecture of K. H. Hofmann and K. Strambach (Problem 6.15 in [Topological and analytic loops, in "Quasigroups and Loops Theory and Applications,"

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