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1.
Igor Dolinka 《Algebra Universalis》2009,60(1):19-35
We give a sufficient condition which ensures that a semiring with an idempotent addition is inherently nonfinitely based.
This enables us to provide a number of small and natural examples of nonfinitely based semirings, including semirings of binary
relations on a finite set.
Supported by Grant No.144011 of the Ministry of Science of the Republic of Serbia. 相似文献
2.
Clifford Bergman 《Order》1989,6(1):49-58
We prove that if v is the variety generated by a finite modular lattice, then v is not an elementary class. We also consider the same question for the variety generated by N
5.Research partially supported by National Science Foundation grant DMS-8701643. 相似文献
3.
We describe the free modular lattice generated by two chains and a single point, under the assumption that there are few meets.
Received February 11, 2005; accepted in final form August 11, 2005. 相似文献
4.
Hugh Thomas 《Algebra Universalis》2005,53(4):481-489
We provide a direct proof that a finite graded lattice with a maximal chain of left modular elements is supersolvable. This result was first established via a detour through EL-labellings in [MT] by combining results of McNamara [Mc] and Liu [Li]. As part of our proof, we show that the maximum graded quotient of the free product of a chain and a single-element lattice is finite and distributive.Received May 24, 2004; accepted in final form October 12, 2004. 相似文献
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There are two natural ways to extend an arbitrary map between (the carriers of) two lattices, to a map between their MacNeille
completions. In this paper we investigate which properties of lattice maps are preserved under these constructions, and for
which kind of maps the two extensions coincide.
Our perspective involves a number of topologies on lattice completions, including the Scott topologies and topologies that
are induced by the original lattice. We provide a characterization of the MacNeille completion in terms of these induced topologies.
We then turn to expansions of lattices with additional operations, and address the question of which equational properties
of such lattice expansions are preserved under various types of MacNeille completions that can be defined for these algebras.
For a number of cases, including modal algebras and residuated (ortho)lattice expansions, we provide reasonably sharp sufficient
conditions on the syntactic shape of equations that guarantee preservation. Generally, our results show that the more residuation
properties the primitive operations satisfy, the more equations are preserved.
Received August 21, 2005; accepted in final form October 17, 2006. 相似文献
7.
Ralph Freese 《Order》1987,3(4):331-344
In the late 1930s Phillip Whitman gave an algorithm for deciding for lattice terms v and u if vu in the free lattice on the variables in v and u. He also showed that each element of the free lattice has a shortest term representing it and this term is unique up to commutivity and associativity. He gave an algorithm for finding this term. Almost all the work on free lattices uses these algorithms. Building on the work of Ralph McKenzie, J. B. Nation and the author have developed very efficient algorithms for deciding if a lattice term v has a lower cover (i.e., if there is a w with w covered by v, which is denoted by w) and for finding them if it does. This paper studies the efficiency of both Whitman's algorithm and the algorithms of Freese and Nation. It is shown that although it is often quite fast, the straightforward implementation of Whitman's algorithm for testing vu is exponential in time in the worst case. A modification of Whitman's algorithm is given which is polynomial and has constant minimum time. The algorithms of Freese and Nation are then shown to be polynomial. 相似文献
8.
Jaroslav Ježek 《Order》1985,2(1):69-79
For any N3 there exists a lattice L isomorphic with NL (the free product of its own N copies) but not isomorphic with kL for any k–2,...,N-1. 相似文献
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10.
Marcel Jackson 《Semigroup Forum》2002,64(2):297-324
We show how to construct all ``forbidden divisors' for the pseudovariety of not inherently nonfinitely based finite semigroups. Several other results concerning finite semigroups that generate an inherently
nonfinitely based variety that is miminal amongst those generated by finite semigroups are obtained along the way. For example,
aside from the variety generated by the well known six element Brandt monoid \tb , a variety of this type is necessarily generated by a semigroup with at least 56 elements (all such semigroups with 56 elements
are described by the main result).
September 23, 1999 相似文献
11.
In this note we prove: If a subdirect product of finitely many finite projective geometries has the cover-preserving embedding property, then so does each factor. 相似文献
12.
Scott R. Sykes 《Algebra Universalis》2007,56(3-4):349-356
The purpose of this paper is to introduce the lattice of convex partitions for a lattice L. Then we will show some properties of this lattice. Finally, we will show that if the convex partition lattice of L is finite and modular if and only if L is a finite chain.
Presented by R. McKenzie.
Received December 16, 2004; accepted in final form March 7, 2006. 相似文献
13.
Christian Herrmann 《Order》1991,8(3):275-281
For modular lattices of finite length, vector space representations are shown to give rise to contracted representations of homomorphic imagesDedicated to the memory of Alan Day 相似文献
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In 1986 Tardos proved that for the poset 1+2+2+2+1, the clone of monotone operations is nonfinitely generated. We generalize his result in the class of series parallel posets. We characterize the posets with nonfinitely generated clones in this class by the property that they have a retract of the form either 1+2+2+2+1, 2+2+1, or 1+2+2.Research partially supported by Hungarian National Foundation for Research under grant no. 1903. 相似文献
16.
Martin Aigner 《Aequationes Mathematicae》1977,16(1-2):37-50
In a geometric lattice every interval can be mapped isomorphically into an upper interval (containing 1) by a strong map. A natural question thus arises as to what extent certain assumptions on the upper interval structure determine the whole lattice. We consider conditions of the following sort: that above a certain levelm any two upper intervals of the same length be isomorphic. This property, called uniformity, is studied for binary geometries. The geometries satisfying the strongest uniformity condition (m = 1) are determined (except for one open case). As is to be expected the corresponding problem for lower intervals is easier and is solved completely. 相似文献
17.
For any finitely based self-dual variety of lattices, we determine the sizes of all equational bases that are both irredundant and self-dual. We make the same determination for {0, 1}-lattice varieties.Received July 11, 2002; accepted in final form August 27, 2004. 相似文献
18.
This paper introduces a new class of lattice ordered algebras. A lattice ordered
algebra A will be called a pseudo f-algebra
if xy = 0 for all x, y in
A such that x y
is a nilpotent element in A. Dierent aspects of archimedean pseudo
f-algebras are considered in detail. Mainly their integral representations on spaces
of continuous functions, as well as their connection with almost f-algebras and
f-algebras. Various characterizations of order bounded multiplicators on pseudo
f-algebras are given, where by a multiplicator on a pseudo
f-algebra A we mean an operator
T on A such that
xT(y) = yT(x) for all x, y
in A. In this regard, it will be focused on the relationship between multiplicators and
orthomorphisms on pseudo f-algebras. 相似文献
19.
Gretchen Wilke Whipple 《Algebra Universalis》2005,54(1):53-63
In this paper we demonstrate that every positive totally ordered commutative monoid on 2 generators satisfying a weak cancellation
property is a convex Rees quotient of a sub-monoid of a totally ordered Abelian group. In [1], the current author, along with
Evans, Konikoff, Mathis, and Madden, employed the work of Hion, [5], to demonstrate that the monoid ring of all finite formal
sums over a totally ordered domain is a formally real totally ordered ring providing the totally ordered monoid satisfies
this weak cancellation property and is a convex Rees quotient of a sub-monoid of a totally ordered Abelian group. Therefore,
we provide here significant information about a condition for the construction of formally real totally ordered monoid algebras.
Received November 4, 2003; accepted in final form November 18, 2004. 相似文献
20.
We introduce a new construction for orders and lattices. This construction is used to create large locally finite lattice varieties with uncountably many subvarieties.Dedicated to the memory of Ivan RivalReceived October 7, 2003; accepted in final form July 13, 2004.This revised version was published online in August 2005 with a corrected cover date. 相似文献