Subdirect product representations of some unary extensions of semilattices

• Autorzy: Płonka J.
• Języki publikacji: EN

Abstrakty

EN

An algebra [...] represents the sequence so = (0, 3, l, l, . . .) if there are no constants in [...], there are exactly 3 distinct essentially unary polynomials in [...] and exactly l essentially n-ary polynomial in [...] for every n > l . It was proved in [4] that an algebra [..] represents the sequence so if and only if it is clone equivalent to a generic of one of three varieties V1, V2, V3, see Section l of [4]. Moreover, some representations of algebras from these varieties by means of semilattice ordered systems of algebras were given in [4] . In this paper we give another, by subdirect products, representation of algebras from V1, V2, V3. Moreover, we describe all subdirectly irreducible algebras from these varieties and we show that if an algebra [...] represents the sequence so, then it must be of cardinality at least 4.

Słowa kluczowe

EN

universal algebra; generic algebra; subdirectly irreducible algebra; semillatice

PL

algebra ogólna; algebra generyczna; algebra nierozkładalna; półkrata

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2008
• Tom: Vol. 41, nr 2
• Strony: 263--272
• Opis fizyczny: Bibliogr. 5 poz.

Twórcy

autor

Płonka J.

• Mathematical Institute of the Polish Academy of Sciences, ul. Kopernika 18, 51-617 Wrocław, Poland,

Bibliografia

• [1] I. Chajda and K. Glazek, A Basic Course on General Algebra, Technical University Press, Zielona Góra, Poland 2000.
• [2] G. Grätzer, Universal Algebra, 2nd ed., Springer-Verlag, New York-Heidelberg-Berlin 1979.
• [3] G. Grätzer and A. Kisielewicz, A survey of some open problems on pn-sequences and free spectra of algebras and varieties, in: A. Romanowska and J. D. H. Smith (Eds.), "Universal Algebra and Quasigroup Theory", Helderman Verlag, Berlin 1992 57-88.
• [4] A. W. Marczak and J. Płonka, Unarily extended semialttices, Asian-European J. Math., in print.
• [5] J. Płonka, On a method of construction of abstract algebras, Fundamenta Math. 61 (1967), 183-189.