ENDOMORPHISMS OF DISTRIBUTIVE LATTICES WITH A QUANTIFIER

Autor:	M. E. Adams, Wieslaw Dziobiak
Rok vydání:	2007
Předmět:	Monoid Discrete mathematics Pure mathematics Endomorphism General Mathematics Bounded function Quantifier elimination Distributive lattice Priestley space Congruence lattice problem Complemented lattice Mathematics
Zdroj:	International Journal of Algebra and Computation. 17:1349-1376
ISSN:	1793-6500 0218-1967
DOI:	10.1142/s0218196707004190
Popis:	Let V be a non-trivial variety of bounded distributive lattices with a quantifier, as introduced by Cignoli in [7]. It is shown that if V does not contain the 4-element bounded Boolean lattice with a simple quantifier, then V contains non-isomorphic algebras with isomorphic endomorphism monoids, but there are always at most two such algebras. Further, it is shown that if V contains the 4-element bounded Boolean lattice with a simple quantifier, then it is finite-to-finite universal (in the categorical sense) and, as a consequence, for any monoid M, there exists a proper class of non-isomorphic algebras in V for which the endomorphism monoid of every member is isomorphic to M.
Databáze:	OpenAIRE
Externí odkaz:	https://explore.openaire.eu/search/publication?articleId=doi_________::0b25165a07133a1f339d127f7638b40f https://doi.org/10.1142/s0218196707004190 Zobrazit plný text záznamu