Geodesic
Free Abelian extensions in the congruence-permutable varieties
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2.

Voir la notice de l'article provenant de la source Library of Science

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 
@article{DMGAA_2002_22_2_a8,
     author = {Zhdanovich, Pavel},
     title = {Free {Abelian} extensions in the congruence-permutable varieties},
     journal = {Discussiones Mathematicae. General Algebra and Applications},
     publisher = {mathdoc},
     volume = {22},
     number = {2},
     year = {2002},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a8/}
}
TY  - JOUR
AU  - Zhdanovich, Pavel
TI  - Free Abelian extensions in the congruence-permutable varieties
JO  - Discussiones Mathematicae. General Algebra and Applications
PY  - 2002
VL  - 22
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a8/
LA  - en
ID  - DMGAA_2002_22_2_a8
ER  - 
%0 Journal Article
%A Zhdanovich, Pavel
%T Free Abelian extensions in the congruence-permutable varieties
%J Discussiones Mathematicae. General Algebra and Applications
%D 2002
%V 22
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a8/
%G en
%F DMGAA_2002_22_2_a8
Zhdanovich, Pavel. Free Abelian extensions in the congruence-permutable varieties. Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2. http://geodesic.mathdoc.fr/item/DMGAA_2002_22_2_a8/

[1] 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.

[2] V.A. Artamonov and S. Chakrabarti, Free solvable algebra in a general congruence modular variety, Comm. Algebra 24 (1996), 1723-1735.

[3] S. Chakrabarti, Homomorphisms of free solvable algebras with one ternary Mal'cev operation (Russian), Uspehi Mat. Nauk 48 (1993), no. 3, 207-208.

[4] R. Freese and R. McKenzie, Commutator theory for congruence modular varieties, Cambridge Univ. Press, Cambridge 1987.

[5] G. Grätzer, Universal Algebra (2nd ed.) Springer-Verlag, New York 1979.

[6] A.G. Pinus, Congruence Modular Varieties (Russian), Irkutsk State University, Irkutsk 1986.

[7] A.P. Zamyatin, Varieties with Restrictions on the Congruence Lattice (Russian), Ural State University, Sverdlovsk 1987.

[8] P.B. Zhdanovich, Free Abelian extensions of ⟨p,S⟩-algebras, 'Universal Algebra and its Applications', Proceedings of the Skornyakov Conference (Volgograd Ped. Univ., 1999), Izdat. 'Peremena', Volgograd 2000, 73-80.

[9] P.B. Zhdanovich, Free Abelian extensions of Sₚ-permutable algebras (Russian), Chebyshevski Sbornik 3 (2002), No. 1 (3), 49-71.