Geodesic
Free Abelian extensions in the congruence-permutable varieties
Discussiones Mathematicae. General Algebra and Applications, Tome 22 (2002) no. 2 Cet article a éte moissonné depuis la source Library of Science

Voir la notice de l'article

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},
     year = {2002},
     volume = {22},
     number = {2},
     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
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
%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.