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1.
Bruno Bosbach 《Semigroup Forum》1982,25(1):111-124
In this paper we consider complete d-semigroups, i. e. d-semigroups with a conditionally complete lattice satisfying the implication:
⋂ai ⇒ xsy = ⋂xa.y. As main results we present: 1. Every complete d-semigroup is archimedean. 2. A d-semigroup is complete iff
its cone is complete. 3. Every archimedean d-semigroup can be embedded into an archimedean d-semigroup with identity 1. 4.
Every complete d-semigroup can be embedded into a complete d-semigroup with identity.
相似文献
2.
3.
For a complete lattice C, we consider the problem of establishing when the complete lattice of complete congruence relations on C is a complete sublattice of the complete lattices of join- or meet-complete congruence relations on C. We first argue that this problem is not trivial, and then we show that it admits an affirmative answer whenever C is continuous for the join case and, dually, co-continuous for the meet case. As a consequence, we prove that if C is continuous then each principal filter generated by a continuous complete congruence on C is pseudocomplemented.
Received January 6, 1998; accepted in final form July 2, 1998. 相似文献
4.
A 6-cycle system of a graph G is an edge-disjoint decomposition of G into 6-cycles. Graphs G, for which necessary and sufficient conditions for existence of a 6-cycle system have been found, include complete graphs and complete equipartite graphs. A 6-cycle system of G is said to be 2-perfect if the graph formed by joining all vertices distance 2 apart in the 6-cycles is again an edge-disjoint decomposition of G, this time into 3-cycles, since the distance 2 graph in any 6-cycle is a pair of disjoint 3-cycles.Necessary and sufficient conditions for existence of 2-perfect 6-cycle systems of both complete graphs and complete equipartite graphs are known, and also of λ-fold complete graphs. In this paper, we complete the problem, giving necessary and sufficient conditions for existence of λ-fold 2-perfect 6-cycle systems of complete equipartite graphs. 相似文献
5.
V. V. Rybakov 《Algebra and Logic》2002,41(5):323-336
The article studies Barwise's information frames and settles the problem of Barwise dealing in finding axiomatizations for the modal logics generated by information frames. We find axiomatic systems for: (i) the modal logic of all complete information frames; (ii) the logic of all sound and complete information frames; (iii) the logic of all hereditary and complete information frames; (iv) the logic of all complete, sound, and hereditary information frames; (v) the logic of all consistent and complete information frames. The notion of weak modal logics is also proposed, and it is shown that the weak modal logics generated by all information frames and by all hereditary information frames are K and K4, respectively. Toward a general theory, we prove that any Kripke complete modal logic is a modal logic of a certain class of information frames, and that every modal logic generated by any given class of complete, rarefied, and fully classified information frames is Kripke complete. 相似文献
6.
Jorge Picado 《Algebra Universalis》2000,44(3-4):325-332
In [5] G. Gr?tzer and E. T. Schmidt raised the problem of characterizing the complete congruence lattices of complete lattices
satisfying the Join-Infinite Distributive Identity (JID) and the Meet-Infinite Distributive Identity (MID) and proved the
theorem: Any complete lattice with more than two elements and with a meet-irreducible zero cannot be represented as the lattice of
complete congruence relations of a complete lattice satisfying the (JID) and (MID). In this note we generalize this result by showing that the complete congruence lattice of every complete lattice satisfying
(JID) and (MID) is a zero-dimensional complete lattice satisfying (JID). Some consequences are discussed.
Received March 6, 2000; accepted in final form September 12, 2000. 相似文献
7.
On bipartite zero-divisor graphs 总被引:1,自引:0,他引:1
A (finite or infinite) complete bipartite graph together with some end vertices all adjacent to a common vertex is called a complete bipartite graph with a horn. For any bipartite graph G, we show that G is the graph of a commutative semigroup with 0 if and only if it is one of the following graphs: star graph, two-star graph, complete bipartite graph, complete bipartite graph with a horn. We also prove that a zero-divisor graph is bipartite if and only if it contains no triangles. In addition, we give all corresponding zero-divisor semigroups of a class of complete bipartite graphs with a horn and determine which complete r-partite graphs with a horn have a corresponding semigroup for r≥3. 相似文献
8.
Huang Qingxue 《高校应用数学学报(英文版)》2003,18(3):352-360
In this paper, a new concept of an optimal complete multipartite decomposition of type 1 (type 2) of a complete n-partite graph Q
n
is proposed and another new concept of a normal complete multipartite decomposition of K
n
is introduced. It is showed that an optimal complete multipartite decomposition of type 1 of K
n
is a normal complete multipartite decomposition. As for any complete multipartite decomposition of K
n
, there is a derived complete multipartite decomposition for Q
n
. It is also showed that any optimal complete multipartite decomposition of type 1 of Q
n
is a derived decomposition of an optimal complete multipartite decomposition of type 1 of K
n
. Besides, some structural properties of an optimal complete multipartite decomposition of type 1 of K
n
are given.
Supported by the National Natural Science Foundation of China (10271110). 相似文献
9.
On the least complete extension of complete subsemilattices 总被引:1,自引:0,他引:1
For a complete sublattice X of a complete lattice C, we consider the problem of the existence of the least complete meet subsemilattice of C having as least complete extension (i.e., the least complete sublattice of C containing it) X. We argue that this problem is not trivial, and we provide two results that, under certain conditions on C and X, give a positive answer to this problem.
Received January 31, 1997; accepted in final form October 23, 1997. 相似文献
10.
V.V. Rybakov 《Archive for Mathematical Logic》2003,42(3):261-277
The paper studies Barwise's information frames and answers the John Barwise question: to find axiomatizations for the modal
logics generated by information frames. We find axiomatic systems for (i) the modal logic of all complete information frames,
(ii) the logic of all sound and complete information frames, (iii) the logic of all hereditary and complete information frames,
(iv) the logic of all complete, sound and hereditary information frames, and (v) the logic of all consistent and complete
information frames. The notion of weak modal logics is also proposed, and it is shown that the weak modal logics generated
by all information frames and by all hereditary information frames are K and K4 respectively. To develop general theory, we prove that (i) any Kripke complete modal logic is the modal logic of a certain
class of information frames and that (ii) the modal logic generated by any given class of complete, rarefied and fully classified
information frames is Kripke complete. This paper is dedicated to the memory of talented mathematician John Barwise.
Received: 7 May 2000 Published online: 10 October 2002
Key words or phrases: Knowledge presentation – Information – Information flow – Information frames – Modal logic-Kripke model 相似文献
11.
A theory T of a language L is 1-model complete (nearly model complete) iff for every formula ρ of L there is a formula ? (χ) of L which is a ??-formula (a Boolean combination of universal formulas) such that T ? ?x [??θ]. The main results of the paper give characterizations of nearly model complete theories and of 1-model complete theories. As a consequence we obtain that a theory T is nearly model complete iff whenever ?? is a model of T and ???1??, then T ∪ Δ1?? is a complete L(A)-theory, where Δ1?? is the 1-diagram of ??. We also point out that our main results extend to (n + l)-model complete and nearly ra-model complete theories for all n > 0. 相似文献
12.
It has been shown by MacGillivray and Seyffarth (Austral. J. Combin. 24 (2001) 91) that bridgeless line graphs of complete graphs, complete bipartite graphs, and planar graphs have small cycle double covers. In this paper, we extend the result for complete bipartite graphs, and show that the line graph of any complete multipartite graph (other than K1,2) has a small cycle double cover. 相似文献
13.
Ilene H. Morgan 《Annals of Combinatorics》1997,1(1):377-389
A complete set of mutually equiorthogonal frequency hypercubes (MEFH) of ordern and dimensiond, usingm distinct symbols, has (n−1)
d
/(m−1) hypercubes. In this article, we explore the properties of complete sets of MEFH. As a consequence of these properties,
we show that existence of such a set implies that the number of symbolsm is a prime power. We also establish an equivalence between existence of a complete set of MEFH and existence of a certain
complete set of Latin hypercubes and a certain complete orthogonal array. 相似文献
14.
15.
Classical reducibilities have complete sets U that any recursively enumerable set can be reduced to U. This paper investigates existence of complete sets for reducibilities with limited oracle access. Three characteristics of classical complete sets are selected and a natural hierarchy of the bounds on oracle access is built. As the bounds become stricter, complete sets lose certain characteristics and eventually vanish. (© 2003 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
16.
Dominic van der Zypen 《Central European Journal of Mathematics》2006,4(3):525-530
We characterise the Priestley spaces corresponding to affine complete bounded distributive lattices. Moreover we prove that
the class of affine complete bounded distributive lattices is closed under products and free products. We show that every
(not necessarily bounded) distributive lattice can be embedded in an affine complete one and that ℚ ∩ [0, 1] is initial in
the class of affine complete lattices. 相似文献
17.
Mohsen Alimohammady Abdolreza Esmaeli Reza Saadati 《Chaos, solitons, and fractals》2009,39(2):765-769
In this paper, we consider complete probabilistic metrizable (topological) space and prove that any Gδ set in a complete probabilistic metric spaces is a topologically complete probabilistic metrizable space. 相似文献
18.
D. G. Rogers 《Discrete Mathematics》1988,70(3):219-240
We develop an arithmetic of complete permutations of symmetric, integral bases; this arithmetic is comparable to that of perfect systems of difference sets with which there are several interrelations. Super-position of permutations provides the addition of this arithmetic. Addition if facilitated by complete permutations with a certain “splitting” property, allowing them to be pulled apart and reassembled. The split permutations also provide a singular direct product for complete permutations in conjunction with the multiplication (direct product) of the arithmetic which itself derives from that for perfect systems of difference sets.
We pay special attention to complete permutations satisfying constraints both fixed and variable; this is equivalent to embedding partial complete permutations in complete permutations. In the sequel, using this arithmetic, we investigate the spectra of certain constraints with respect to central integral bases which are of interest for the purpose of giving further constructions either of complete permutations with constraints or of irregular, extremel perfect systems of difference sets. 相似文献
19.
Larry D Gassman R.C Entringer John R Gilbert Stephen A Lonz Wayne Vucenic 《Journal of Combinatorial Theory, Series B》1975,19(3):214-238
Ore defined a graph to be geodetic if and only if there is a unique shortest path between two points, and posed the problem of characterizing such graphs. Here this problem is studied in the context of oriented graphs and such geodetic orientations are characterized first for complete graphs (geodetic tournaments), then for complete bipartite and complete tripartite graphs, and finally for complete k-partite graphs. 相似文献
20.
AbstractIn this article, we investigate some basic results on complete hom-Lie superalgebras. In particular, we present some sufficient conditions for a hom-Lie superalgebra to be a complete hom-Lie superalgebra. Making use of these conditions, we build a family of complete hom-Lie superalgebras. 相似文献