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1.
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
2.
In this paper we provide sufficient conditions on a given finite algebra to prevent it from being strongly dualizable. We
then use these conditions to prove that certain unary algebras are not strongly dualizable.
This paper is dedicated to Walter Taylor.
Received November 16, 2005; accepted in final form May 12, 2006. 相似文献
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The research of the first two authors was supported by the NSERC of Canada. 相似文献
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R. Baer asked whether the group operation of every (totally) ordered group can be redefined, keeping the same ordered set, so that the resulting structure is an Abelian ordered group. The answer is no. We construct an ordered set (G, ) which carries an ordered group (G, , ) but which islawless in the following sense. If (G, *, ) is an ordered group on the same carrier (G, ), then the group (G, *) satisfies no nontrivial equational law.Research partially supported by NSERC of Canada Grants #A4044 and A3040.Research partially supported by NSERC of Canada Grant #U0075.Research partially supported by a grant from the BSF. 相似文献
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I. Chajda 《Periodica Mathematica Hungarica》1989,20(4):241-248
12.
Brian A. Hagler 《Linear algebra and its applications》2007,422(1):100-118
Definitions, theorems and examples are established for a general model of Laurent polynomial spaces and ordered orthogonal Laurent polynomial sequences, ordered with respect to ordered bases and orthogonal with respect to inner products ·=L°⊙ decomposed into transition functional ⊙ and strong moment functional, or, more generally, sample functional L couplings. Under this formulation that is shown to subsume those in the existing literature, new fundamental results are produced, including necessary and sufficient conditions for ordered OLPS to be sequences of nth numerators of continued fractions, in contrast to the classical result concerning nth denominators which is shown to hold only in special cases. 相似文献
13.
Todd Niven 《Algebra Universalis》2007,57(1):101-107
Let
be a finite algebra. We show that if there exists a particular dualising alter ego
that satisfies a weak form of injectivity, then the notions of full duality and strong duality for
are equivalent.
Presented by R. Willard.
Received August 30, 2005; accepted in final form August 1, 2006. 相似文献
14.
Cancellative residuated lattices are natural generalizations of lattice-ordered
groups (
-groups).
Although cancellative monoids are defined by quasi-equations, the class
of cancellative residuated lattices is a variety.
We prove that there are only two
commutative subvarieties of
that cover the trivial variety, namely the varieties
generated by the integers and the negative integers (with zero). We also construct examples
showing that in contrast to
-groups, the lattice reducts of cancellative residuated lattices
need not be distributive. In fact we prove that every lattice can be embedded in the
lattice reduct of a cancellative residuated lattice. Moreover, we show that there exists an
order-preserving injection of the lattice of all lattice varieties into the subvariety lattice of
.We define generalized MV-algebras and generalized BL-algebras and prove that the
cancellative integral members of these varieties are precisely the negative cones of
-groups, hence the latter form a variety, denoted by
. Furthermore we prove that the map that sends a subvariety of
-groups to the corresponding class of negative cones is a lattice
isomorphism from the lattice of subvarieties of
to the lattice of subvarieties of
.
Finally, we show how to translate equational bases between corresponding subvarieties, and
briefly discuss these results in the context of R. McKenzies characterization of categorically
equivalent varieties. 相似文献
15.
Richard Holzer 《Algebra Universalis》2007,57(4):419-453
Greechie diagrams are well known graphical representations of orthomodular partial algebras, orthomodular posets and orthomodular
lattices. For each hypergraph D a partial algebra ⟦D⟧ = (A; ⊕, ′, 0) of type (2,1,0) can be defined. A Greechie diagram can be seen as a special hypergraph: different points of the
hypergraph have different interpretations in the corresponding partial algebra ⟦D⟧, and each line in the hypergraph has a maximal Boolean subalgebra as interpretation, in which the points are the atoms.
This paper gives some generalisations of the characterisations in [K83] and [D84] of diagrams which represent orthomodular
partial algebras (= OMAs), and we give an algorithm how to check whether a given hypergraph D is an OMA-diagram whose maximal Boolean subalgebras are induced by the lines of the hypergraph.
Received July 22, 2004; accepted in final form February 1, 2007. 相似文献
16.
Annika M. Wille 《Archiv der Mathematik》2006,87(6):546-553
It will be shown that the word problem is undecidable for involutive residuated lattices, for finite involutive residuated
lattices and certain related structures like residuated lattices. The proof relies on the fact that the monoid reduct of a
group can be embedded as a monoid into a distributive involutive residuated lattice. Thus, results about groups by P. S. Novikov
and W. W. Boone and about finite groups by A. M. Slobodskoi can be used. Furthermore, for any non-trivial lattice variety
, the word problem is undecidable for those involutive residuated lattices and finite involutive residuated lattices whose
lattice reducts belong to
. In particular, the word problem is undecidable for modular and distributive involutive residuated lattices.
The author would like to thank the Deutsche Telekom Stiftung for financial support.
Received: 10 November 2005 相似文献
17.
George Voutsadakis 《Algebra Universalis》2006,55(2-3):369-386
It is very well known and permeating the whole of mathematics that a closure operator on a given set gives rise to a closure
system, whose constituent sets form a complete lattice under inclusion, and vice-versa. Recent work of Wille on triadic concept
analysis and subsequent work by the author on polyadic concept analysis led to the introduction of complete trilattices and
complete n-lattices, respectively, that generalize complete lattices and capture the order-theoretic structure of the collection of
concepts associated with polyadic formal contexts. In the present paper, polyadic closure operators and polyadic closure systems
are introduced and they are shown to be in a relationship similar to the one that exists between ordinary (dyadic) closure
operators and ordinary (dyadic) closure systems. Finally, the algebraic case is given some special consideration.
This paper is dedicated to Walter Taylor.
Received March 10, 2005; accepted in final form March 7, 2006. 相似文献
18.
19.
L.D. Nel 《Topology and its Applications》1981,12(3):321-330
It is shown that a development of universal topological algebra, based in the obvious way on the category of topological spaces, leads in general to a pathological situation. The pathology disappears when the base category is changed to a cartesian closed topological category or to a topological category endowed with a compatible closed symmetric monoidal structure, provided that in the latter case, the algebraic operations are expressed in terms of monoidal powers rather than the usual cartesian powers. With such base categories, universal topological algebra becomes virtually as well-behaved as ordinary (setbased) universal algebra. 相似文献
20.
We show that the 2-crown is not coproductive, which is to say that the class of those bounded distributive lattices whose
Priestley spaces lack any copy of the 2-crown is not productive. We do this by first exhibiting a general construction to
handle questions of this sort. We then use a particular instance of this constrution, along with some of the combinatorial
features of projective planes, to show that the 2-crown is not coproductive.
This paper is dedicated to Walter Taylor.
Received November 24, 2004; accepted in final form July 16, 2005.
The first author would like to express his thanks for support by project LN 00A056 of the Ministry of Education of the Czech
Republic. The second author would like to express his thanks for support by project LN 00A056 of the Ministry of Education
of the Czech Republic, by the NSERC of Canada and by the Gudder Trust of the University of Denver. The third author would
like to express his thanks for support by the NSERC of Canada and partial support by project LN 00A056 of the Ministry of
Education of the Czech Republic. 相似文献