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1.
In [1] R. Beazer characterized affine complete Stone algebras having a smallest dense element. We remove this latter assumption and describe affine complete algebras in the class of all Stone algebras.Dedicated to the memory of M. KolibiarPresented by Á. Szendrei. 相似文献
2.
The finite endodualisable double Stone algebras are characterised, and every finite endoprimal double Stone algebra is shown
to be endodualisable.
The authors wish to express their gratitude to B. A. Davey and T. Katriňák for their helpful remarks and to J. G. Pitkethly
for her assistance with the pictures. A support by Slovak grants VEGA 1/4057/97, 1/3026/06 and APVV-51-009605 is acknowledged
by the first author who also wishes to thank the Mathematical Institute of the University of Oxford and the School of Mathematical
and Statistical Sciences of La Trobe University for their hospitality. 相似文献
3.
A universal algebra isaffine complete if all functions satisfying the Substitution Property are polynomials (composed of the basic operations and the elements of the algebra). In 1962, the first author proved that a bounded distributive lattice is affine complete if and only if it does not contain a proper Boolean interval. Recently, M. Ploica generalized this result to arbitrary distributive lattices.In this paper, we introduce a class of functions on a latticeL, we call themID-polynomials, that derive from polynomials on the ideal lattice (resp., dual ideal lattice) ofL; they are isotone functions and satisfy the Substitution Property. We prove that for a distributive latticeL, all unary functions with the Substitution Property are ID-polynomials if and only ifL contains no proper Boolean interval.The research of the first author was supported by the NSERC of Canada. The research of the second author was supported by the Hungarian National Foundation for Scientific Research, under Grant No. 1903. 相似文献
4.
C. Mendes 《Algebra Universalis》2005,54(3):279-290
An Ockham algebra
that satisfies the identity
is called a Kn, m-algebra. Generalizing some results obtained in [2], J. Varlet and T. Blyth, in [3, Chapter 8], study congruences on K1, 1-algebras. In particular, they describe the complement (when it exists) of a principal congruence and characterize these congruences
that are complemented. In this paper we study the same question for Kn, m-algebras.
Received March 24, 2005; accepted in final form April 28, 2005. 相似文献
5.
6.
We show that if two finite algebras generate the same quasivariety and one is
strongly dualizable, then the other is also strongly dualizable. 相似文献
7.
We call a latticeL strictly locally order-affine complete if, given a finite subsemilatticeS ofL
n, every functionf: S L which preserves congruences and order, is a polynomial function. The main results are the following: (1) all relatively complemented lattices are strictly locally order-affine complete; (2) a finite modular lattice is strictly locally order-affine complete if and only if it is relatively complemented. These results extend and generalize the earlier results of D. Dorninger [2] and R. Wille [9, 10]. 相似文献
8.
This paper investigates endoprimal algebras using techniques from universal
algebra but not from duality theory, and thereby exposes quite directly how endoprimality
occurs. 相似文献
9.
10.
Andrei Popescu 《Algebra Universalis》2005,53(1):73-108
We introduce MV-relation algebras (MVRAs) and distributive MV-relation algebras (DMVRAs), many-valued generalizations of classical relation algebras and study some of their arithmetical properties. We provide corresponding notions of group relation algebra and complex algebra and generalize some results about them from the classical case. For this, we work with more general structures than MVRAs and DMVRAs, by replacing the MV part with a BL-algebra, obtaining what we call fuzzy relation algebras and distributive fuzzy relation algebras.Dedicated to the Memory of Wim BlokReceived February 12, 2003; accepted in final form October 15, 2004.This revised version was published online in August 2005 with a corrected cover date. 相似文献
11.
Abstracting from certain properties of the implication operation in Boolean algebras leads to so-called orthomodular implication algebras. These are in a natural one-to-one correspondence with families of orthomodular lattices. It is proved that congruence kernels of orthomodular implication algebras are in a natural one-to-one correspondence with families of compatible p-filters on the corresponding orthomodular lattices. 相似文献
12.
We investigate ways in which certain binary homomorphisms of a finite algebra can guarantee its dualisability. Of particular interest are those binary homomorphisms which are lattice, flat-semilattice or group operations. We prove that a finite algebra which has a pair of lattice operations amongst its binary homomorphisms is dualisable. As an application of this result, we find that every finite unary algebra can be embedded into a dualisable algebra. We develop some general tools which we use to prove the dualisability of a large number of unary algebras. For example, we show that the endomorphisms of a finite cyclic group are the operations of a dualisable unary algebra. 相似文献
13.
Miroslav Ploščica 《Order》1996,13(3):295-311
For any distributive lattice L we construct its extension ((L)) with the property that every isotone compatible function on L can be interpolated by a polynomial of ((L)). Further, we characterize all extensions with this property and show that our construction is in some sense the simplest possible.This research was supported by the GA SAV Grant 1230/95. 相似文献
14.
Miroslav Ploščica 《Order》1994,11(4):385-390
We prove a characterization theorem for affine complete distributive lattices. To do so we introduce the notions of almost principal ideal and almost principal.This research was supported by GA SAV Grant 362/93. 相似文献
15.
Michael Pinsker 《Algebra Universalis》2004,51(2-3):235-255
16.
We give a duality for the variety of bounded distributive lattices that is not full (and therefore not strong) although it
is full but not strong at the finite level. While this does not give a complete solution to the “Full vs Strong” Problem,
which dates back to the beginnings of natural duality theory in 1980, it does solve it at the finite level. One consequence
of this result is that although there is a Duality Compactness Theorem, which says that if an alter ego of finite type yields
a duality at the finite level then it yields a duality, there cannot be a corresponding Full Duality Compactness Theorem.
Received October 1, 2002; accepted in final form November 10, 2004. 相似文献
17.
18.
Let be a finitely generated variety of Heyting algebras and let be the class of subdirectly irreducible algebras in . We prove that is dually equivalent to a category of functors from into the category of Boolean spaces. The main tool is the theory of multisorted natural dualities. 相似文献
19.
In this paper we study the direct decomposability of free Tarski algebras. We
show that infinite freely generated Tarski algebras are directly indecomposable, whereas
finite freely generated Tarski algebras can only be decomposed into a direct product of two
factors, one of which is the two-element Tarski algebra. 相似文献
20.
Jenó Szigeti 《Order》1990,7(1):77-81
Given a linearly ordered set (A,
R
) and an R-monotone function f: AA, we give a necessary and sufficient condition on A, f,
R
, involving generating sets and forbidden subalgebras, for
R
to be a well-ordering.Partially supported by Hungarian National Foundation for Scientific Research Grant nr. 1813. 相似文献