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Distributive multisemilattices

Seria
Rozprawy Matematyczne tom/nr w serii: 309 wydano: 1991
Zawartość
Warianty tytułu
Abstrakty
EN
A distributive multisemilattice of type n is an algebra with a family of n binary semilattice operations on a common carrier that are mutually distributive. This concept for n=2 comprises the distributive bisemilattices (or quasilattices), of which distributive lattices and semilattices with duplicated operations are the best known examples. Multisemilattices need not satisfy the absorption law, which holds in all lattices.
Kalman has exhibited a subdirectly irreducible distributive bisemilattice which is neither a lattice nor a semilattice. It has three elements. In this paper it is shown that all the subdirectly irreducible distributive multisemilattices are derived from those for n=2 simply by duplicating their operations in all possible ways. Thus, up to isomorphism there are $2^{n}-1$ of type n, but up to the coarser relation of polynomial equivalence there are only three. Hence every distributive multisemilattice is the subdirect product of irreducibles, each with two or three elements.
The rest of the paper is devoted to the varieties of distributive multisemilattices. The lattice of these varieties is described, and bases for their identities are given.
EN

CONTENTS
1. Introduction........................................................................................................................5
2. Definition, basic examples and properties of multisemilattices...........................................6
3. The subdirectly irreducibles..............................................................................................13
4. The lattice of subvarieties of $D_n$.................................................................................18
5. Subvarieties of $D_n$ defined by identities involving at most two operation symbols......24
6. Some further comments and open problems....................................................................34
References...........................................................................................................................40
Miejsce publikacji
Warszawa
Copyright
Seria
Rozprawy Matematyczne tom/nr w serii: 309
Liczba stron
42
Liczba rozdzia³ów
Opis fizyczny
Dissertationes Mathematicae, Tom CCCIX
Daty
wydano
1991
otrzymano
1990-05-31
Twórcy
  • Department of Mathematical Sciences, New Mexico State University, Las Cruces, New Mexico 88003, U.S.A.
  • Institute of Mathematics, Warsaw Technical University, 00-661 Warszawa, Poland
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Języki publikacji
EN
Uwagi
1985 Mathematics Subject Classification: Primary 06A12, 08B15; Secondary 05C40, 08B05.
Identyfikator YADDA
bwmeta1.element.zamlynska-553ea7ba-6a08-4b20-8ee7-4c4ed1ce33b2
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ISBN
83-85116-09-5
ISSN
0012-3862
Kolekcja
DML-PL
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