TL;DR
This paper constructs a basis for the free Malcev algebra with three generators over a field of characteristic zero, proving its structural properties and decomposability into known algebraic components.
Contribution
It provides the first explicit basis for the free Malcev algebra of rank three and demonstrates its decomposability into free Lie and Malcev algebras.
Findings
Basis of the free Malcev algebra of rank three established
Proved the algebra's specialty and semiprimitivity
Showed decomposability into subdirect sum of known algebras
Abstract
We find a basis of the free Malcev algebra on three free generators over a field of characteristic zero. The specialty and semiprimity of this algebra are proved. In addition, we prove the decomposability of this algebra into subdirect sum of the free Lie algebra rank three and the free algebra of rank three of variety of Malcev algebras generated by a simple seven-dimensional Malcev algebra.
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