Discussiones Mathematicae General Algebra and Applications 22(2) (2002) 199-216
doi: 10.7151/dmgaa.1058

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Pavel Zhdanovich

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.


V.A. Artamonov, Magnus representation in congruence modular varieties (Russian), Sibir. Mat. Zh. 38 (1997), 978-995 (English transl. in Siberian Math. J. 38 (1997), 842-859.).
V.A. Artamonov and S. Chakrabarti, Free solvable algebra in a general congruence modular variety, Comm. Algebra 24 (1996), 1723-1735.
S. Chakrabarti, Homomorphisms of free solvable algebras with one ternary Mal'cev operation (Russian), Uspehi Mat. Nauk 48 (1993), no. 3, 207-208.
R. Freese and R. McKenzie, Commutator theory for congruence modular varieties, Cambridge Univ. Press, Cambridge 1987.
G. Grätzer, Universal Algebra (2nd ed.) Springer-Verlag, New York 1979.
A.G. Pinus, Congruence Modular Varieties (Russian), Irkutsk State University, Irkutsk 1986.
A.P. Zamyatin, Varieties with Restrictions on the Congruence Lattice (Russian), Ural State University, Sverdlovsk 1987.
P.B. Zhdanovich, Free Abelian extensions of ⟨p, S⟩-algebras, p. 73-80 in the book "Universal Algebra and its Applications", Proceedings of the Skornyakov Conference (Volgograd Ped. Univ., 1999), Izdat. "Peremena", Volgograd 2000.
P.B. Zhdanovich, Free Abelian extensions of Sp-permutable algebras (Russian), Chebyshevski Sbornik 3 (2002), No. 1 (3), 49-71.

Received 23 December 2002
Revised 13 January 2003
Revised 13 February 2003