Mathematicae General Algebra and Applications 22(2) (2002)
FREE ABELIAN EXTENSIONS IN THE CONGRUENCE-PERMUTABLE VARIETIES
Volgograd State Pedagogical University, Russia
We obtain the construction of free abelian extensions in a congurence-permutable variety V
using the construction of a free abelian extension in a variety of algebras with one ternary Mal'cevoperation
and a monoid of unary operations. We also use this construction to obtain a free solvable V-algebra.
Keywords: abelian extension, solvable algebra, congurence-permutable variety.
2000 Mathematics Subject Classification: 08B10, 08B20.
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Received 23 December 2002
Revised 13 January 2003
Revised 13 February 2003