The Freiheitssatz and the automorphisms of free right-symmetric algebras
Daniyar Kozybaev, Leonid Makar-Limanov, Ualbai Umirbaev
TL;DR
This paper establishes fundamental algebraic properties for right-symmetric algebras, including the Freiheitssatz, decidability of the word problem, and characterizations of subalgebras and automorphisms, advancing understanding of their structure.
Contribution
It proves the Freiheitssatz and decidability of the word problem for right-symmetric algebras, and characterizes subalgebras and automorphisms of free right-symmetric algebras.
Findings
Freiheitssatz holds for right-symmetric algebras
Word problem is decidable with one defining relation
Subalgebras generated by two elements are free and automorphisms are tame
Abstract
We prove the Freiheitssatz for right-symmetric algebras and the decidability of the word problem for right-symmetric algebras with a single defining relation. We also prove that two generated subalgebras of free right-symmetric algebras are free and automorphisms of two generated free right-symmetric algebras are tame.
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