On some sets of identities satisfied in Abelian groups

• Autorzy: Gajewska-Kurdziel K. , Mruczek K.
• Języki publikacji: EN

Abstrakty

EN

The equational theories were studied in many works (see [4], [5], [6], [7]). Let T be a type of Abelian groups. In this paper we consider the extentions of the equational theory Ex(Gn) defined by so called externally compatible identities of Abelian groups and the identity xn = yn. The equational base of this theory was found in [3]. We prove that each equational theory Cn(Ex^(Gn) U {(phi=epsilon}), where phi=epsilon is an identity of type r, is equal to the extension of the equational theory Cn{Ex{Gn) U E), where E is a finite set of one variable identities of type r. The notation in this paper are the same as in [1].

Słowa kluczowe

EN

abelian group; equational theory

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2002
• Tom: Vol. 35, nr 3
• Strony: 447--453
• Opis fizyczny: Bibliogr. 7 poz.

Twórcy

autor

Gajewska-Kurdziel K.

• University of Opole, Institute of Mathematics and Computer Science, ul. Oleska 48 45-052 Opole, Poland

autor

Mruczek K.

• University of Opole, Institute of Mathematics and Computer Science, ul. Oleska 48 45-052 Opole, Poland

Bibliografia

• [1] S. Burris, H. P. Sankappanavar, A Course in Universal Algebra, Springer, New York 1981.
• [2] W. Chromik, Externally compatible identities of algebras, Demonstratio Math. 23 (1990), 344-355.
• [3] K. Hałkowska, B. Cholewińska, R. Wiora, Externally compatible identities of Abelian groups, Acta Univ. Wratislav. No 1890 (1997), 163-170.
• [4] J. Ježek, The lattice of equational theories, Part I, Part II, Part III, Czeh. Math. J. 31 (1981) 127-157, 31 (1981), 573-603, 32 (1982), 129-164.
• [5] B. Jónnson, Equational classes of lattices, Math. Scand. 22 (1968), 187-196.
• [6] R. McKenzie, Equational bases and non-modular lattice varieties, Trans. Amer. Math. Soc. 174 (1972), 1-43.
• [7] G. F. McNulty, Structural diversity in the lattice of equational theories, Algebra Universalis 13 (1981), 271-292.