P-compatible Abelian groups
DOI:
https://doi.org/10.12775/LLP.2005.016Keywords
Abelian groups, P-compatible identity, variety, partition of a setAbstract
Let τ : F → N be a type of a variety V . Every partition P of the set F determines a so-called P-compatible variety. We consider the varieties GnP defined by so-called P-compatible identities of Abelian groups with exponent n. Besides, we study a connection between the lattice of all partitions of the set F and the lattice of all subvarieties of the variety defined by some kind of P-compatible identities — externally compatible identities satisfied in the class of all Abelian groups with exponent n.
References
Chromik, W., “On externally compatible identities of algebras”, Demonstratio Mathematica 23(2): 345–355, 1990.
Gajewska-Kurdziel, K., “On the lattices of some warieties defined by externally compatible identities”. In: K. Denecke, (ed.), General ALgebra and Discrete Mathematics, Heldermann-Verlag, Berlin, (1995), pp. 107–110.
Hałkowska, K., “On free algebras in varieties defined by externally compatible identities”. In: K. Hałkowska and B. Stawski, (eds.), Universal and applied algebra, Proceedings of the V Universal Algebra Symposium, World Scientific, Singapore, 1988, pp. 143–148.
Hałkowska, K., “Lattice of equational theories of P-compatible varieties”. In: E. Orłowska, (ed.), Logic at Work. Essays dedicated to the memory of Helena Rasiowa, Heidelberg, New York, Springer, 1998, pp. 587–595.
Mel’nik, I.J., “Nilpotent shifts of varieties” (in Russian), Mat. Zametki 14, 5 (1973). English translation: Math. Notes 14: 962–966, 1973.
Mruczek, K., “On some lattice of varieties related to changes of the type”. In: K. Denecke and H.-J. Vogel, (eds.), General Algebra and Applications, Proceedings of the 59th Workshop on General Algebra, Shaker Verlag, Aachen, 2000, pp. 147–153.
Płonka, J., “On equational classes of abstract algebras defined by regular equations”, Fund. Math. 64: 241–147, 1969.
Płonka, J., “On the subdirect product of some equational classes of algebras”, Math. Nachr. 63: 303–305, 1974.
Płonka, J., “P-compatible identities and their applications to classical algebras”, Math. Slovaca 40(1): 21–30, 1990.
Płonka, J., “On varieties of algebras defined by identities of some special forms”, Houston Jurnal of Math. 14: 253–263, 1988.
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