Free Abelian extensions in the congruence-permutable varieties

Pavel Zhdanovich

Discussiones Mathematicae - General Algebra and Applications (2002)

  • Volume: 22, Issue: 2, page 199-216
  • ISSN: 1509-9415

Abstract

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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.

How to cite

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Pavel Zhdanovich. "Free Abelian extensions in the congruence-permutable varieties." Discussiones Mathematicae - General Algebra and Applications 22.2 (2002): 199-216. <http://eudml.org/doc/287701>.

@article{PavelZhdanovich2002,
abstract = {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.},
author = {Pavel Zhdanovich},
journal = {Discussiones Mathematicae - General Algebra and Applications},
keywords = {abelian extension; solvable algebra; congurence-permutable variety; congruence modular variety},
language = {eng},
number = {2},
pages = {199-216},
title = {Free Abelian extensions in the congruence-permutable varieties},
url = {http://eudml.org/doc/287701},
volume = {22},
year = {2002},
}

TY - JOUR
AU - Pavel Zhdanovich
TI - Free Abelian extensions in the congruence-permutable varieties
JO - Discussiones Mathematicae - General Algebra and Applications
PY - 2002
VL - 22
IS - 2
SP - 199
EP - 216
AB - 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.
LA - eng
KW - abelian extension; solvable algebra; congurence-permutable variety; congruence modular variety
UR - http://eudml.org/doc/287701
ER -

References

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  1. [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. Zbl0905.08004
  2. [2] V.A. Artamonov and S. Chakrabarti, Free solvable algebra in a general congruence modular variety, Comm. Algebra 24 (1996), 1723-1735. Zbl0858.08005
  3. [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. [4] R. Freese and R. McKenzie, Commutator theory for congruence modular varieties, Cambridge Univ. Press, Cambridge 1987. Zbl0636.08001
  5. [5] G. Grätzer, Universal Algebra (2nd ed.) Springer-Verlag, New York 1979. 
  6. [6] A.G. Pinus, Congruence Modular Varieties (Russian), Irkutsk State University, Irkutsk 1986. 
  7. [7] A.P. Zamyatin, Varieties with Restrictions on the Congruence Lattice (Russian), Ural State University, Sverdlovsk 1987. Zbl0692.08001
  8. [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. [9] P.B. Zhdanovich, Free Abelian extensions of Sₚ-permutable algebras (Russian), Chebyshevski Sbornik 3 (2002), No. 1 (3), 49-71. Zbl1104.08002

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