共查询到18条相似文献,搜索用时 578 毫秒
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王军涛 《高校应用数学学报(A辑)》2021,36(1):111-126
引入了相似剩余格的概念,讨论了剩余格上相似算子和等价算子的关系,并得到了真值剩余格和相似剩余格相互转化的方法.其次,研究了相似剩余格上的相似滤子,利用相似滤子刻画了可表示的相似剩余格.最后,引入了相似剩余格对应的逻辑系统,证明了其完备性定理,并得到了其成为半线性逻辑的条件. 相似文献
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本文证明了格的极小生成元集一定是最小生成元集且只能是非零完全并既约元全体,证明了分配格具有最小生成元集的必要条件是它满足并无限分配律.本文还证明了完全Heyting代数具有最小生成元集当且仅当它是强代数格,证明了完备格是强代数格当且仅当它和它的对偶格均是具有最小生成元集的分配格. 相似文献
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对完备格引入半素极小集的概念,证明完备格L为半连续格当且仅当L中的每个元在L中存在半素极小集,给出半连续格的两个序同态扩张定理. 相似文献
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ψ—连续格的刻划与完全分配格的拓扑表示定理 总被引:2,自引:0,他引:2
本文在完备格中引入ψ-S集的概念,并在讨论ψ-S集族性质的基础上给出-ψ-连续格的一族拓扑及格论刻划,用局部超紧的Sober空间范畴给出完全分配格的拓扑表示定理。 相似文献
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指出了软代数现行表示的非自然性;通过引入新的集对F格与伪幂集格,获得了两个自然的软代数表示定理,并证明了它们在某种意义上不可能再改进. 相似文献
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John W. Snow 《Algebra Universalis》2000,43(2-3):279-293
A finite lattice is representable if it is isomorphic to the congruence lattice of a finite algebra. In this paper, we develop methods by which we can construct
new representable lattices from known ones. The techniques we employ are sufficient to show that every finite lattice which
contains no three element antichains is representable. We then show that if an order polynomially complete lattice is representable
then so is every one of its diagonal subdirect powers.
Received August 30, 1999; accepted in final form November 29, 1999. 相似文献
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A. I. Budkin 《Algebra Universalis》2001,46(1-2):15-24
It is found the necessary condition for the lattice of quasivarieties has a finite set of coatoms. In particular if a quasivariety
is generated by a finitely generated abelian-by-polycyclic-by-finite group or a totally ordered group then it has a finite
set of proper maximal subquasivarieties. Also it is proved that the set of quasiverbal congruence relations of a finitely
defined universal algebra is closed under any meets.
Received March 23, 1999; accepted in final form June 7, 1999. 相似文献
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It is proved that the collection of all finite lattices with the same partially ordered set of meet-irreducible elements can be ordered in a natural way so that the obtained poset is a lattice. Necessary and sufficient conditions under which this lattice is Boolean, distributive and modular are given. 相似文献
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For any ordered set P, the join dense completions of P form a complete lattice K(P) with least element O(P), the lattice of order ideals of P, and greatest element M(P), the Dedekind–MacNeille completion P. The lattice K(P) is isomorphic to an ideal of the lattice of all closure operators on the lattice O(P). Thus it inherits some local structural properties which hold in the lattice of closure operators on any complete lattice. In particular, if K(P) is finite, then it is an upper semimodular lattice and an upper bounded homomorphic image of a free lattice, and hence meet semidistributive. 相似文献
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本文建立了并素元有限生成格的弱直积分解,并给出一个解决并素元生成的完全Heyting代数的直积分解问题的新方法;作为弱直积分解的应用,证明了并素元有限生成的完全Heyting代数必然同构于有限个既约的完全Heyting代数的直积,证明了并素元有限生成格是Boole代数的充要条件是它同构于某有限集的幂集格. 相似文献
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Bordalo Gabriela Caspard Nathalie Monjardet Bernard 《Czechoslovak Mathematical Journal》2009,59(1):249-271
In this paper we first study what changes occur in the posets of irreducible elements when one goes from an arbitrary Moore
family (respectively, a convex geometry) to one of its lower covers in the lattice of all Moore families (respectively, in
the semilattice of all convex geometries) defined on a finite set. Then we study the set of all convex geometries which have
the same poset of join-irreducible elements. We show that this set—ordered by set inclusion—is a ranked join-semilattice and
we characterize its cover relation. We prove that the lattice of all ideals of a given poset P is the only convex geometry having a poset of join-irreducible elements isomorphic to P if and only if the width of P is less than 3. Finally, we give an algorithm for computing all convex geometries having the same poset of join-irreducible
elements.
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A relation algebra is called measurable when its identity is the sum of measurable atoms, where an atom is called measurable if its square is the sum of functional elements.In this paper we show that atomic measurable relation algebras have rather strong structural properties: they are constructed from systems of groups, coordinated systems of isomorphisms between quotients of the groups, and systems of cosets that are used to “shift” the operation of relative multiplication. An atomic and complete measurable relation algebra is completely representable if and only if there is a stronger coordination between these isomorphisms induced by a scaffold (the shifting cosets are not needed in this case). We also prove that a measurable relation algebra in which the associated groups are all finite is atomic. 相似文献