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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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引入偏序集的相对极大滤子的概念,证明在任意条件交半格中一个滤子是相对极大滤子当且仅当它是滤子格的完全交不可约元.一个格是分配的当且仅当每一个相对极大滤子都是素滤子.随后研究了Heyting代数中相对极大滤子的刻画,最后定义和研究了完全并既约生成格. 相似文献
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文章先利用自同构映射保有限并的性质研究了一般正交模格的次直积的自同构群与自同构群的次直积的关系,再用块置换的方法研究了MOk的自同构群的生成元集,由此得到自由正交模格FMOk(n)的自同构群的直积分解式,从而完全解决了FMOk(n)的自同构群的结构问题. 相似文献
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完备强对偶原子分配格上的不可约极小并分解及其应用 总被引:3,自引:0,他引:3
在完备强对偶原子分配格上引入了不可约极小并分解的概念,给出了元素存在不可约极小并分解的一些充要条件.证明了当元素恰有一个下邻时,该元索就足完全并既约元;有两个下邻时,元素的不可约极小并分解与不可约完全并既分解是等价的;下邻多于两个时,元素的不可约极小并分解不一定足不可约完全并既分解.最后证明了模糊关系方程有极小解的充要条件是方程左边有大于等于右手项的系数或右手项系数有不可约极小并分解. 相似文献
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针对分配格与模格的格等式定义问题,得知了二条件是定义分配格与模格的最少条件,并进一步证明了Sholander's basis是定义分配格的最短最少变量格等式,最后又从分配格和模格的基本定义出发给出了新的分配格的二条件和三条件等价定义等式及模格的二条件与三条件等价定义等式. 相似文献
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一类完备格的直积分解与Fuzzy格的构造 总被引:3,自引:0,他引:3
本文主要结果为:1.以拓扑空间的连通分支为工具,证明了由并素元生成的完全Heyting代数存在既约的直积分解,并且它的任意两个既约直积分解是等价的,从而推广了[1]的主要结果;2.利用完全分配格的既约直积分解,得到Fuzzy格的一个构造定理,并在此基础上讨论Fuzzy格的直积分解,证明了任一Fuzzy格存在既约直积分解,并在序同构的意义下是唯一的. 相似文献
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设L是赋范线性空间上的子空间格,一个子空间是自反AlgL-模的充分必要条件被得到,当L是完全分配子空间格时,自反AlgL-模的二次交换子被描述,进而,本文引入V-生成子稠格,这是一种严格地包含了完全分配格和五角格的格类。当L是可换的V-生成子稠格时,模模交换子C(AlgL;M)和代数AlgLatM都被分解成直和,并且满足条件H~1(AlgL,B(H))=0的一阶上同调空间H~1(AlgL,M)被刻划。 相似文献
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Hugh Thomas 《Order》2006,23(2-3):249-269
In this paper, we study lattices that posess both the properties of being extremal (in the sense of Markowsky) and of being left modular (in the sense of Blass and Sagan). We call such lattices trim and show that they posess some additional appealing properties, analogous to those of a distributive lattice. For example, trimness is preserved under taking intervals and suitable sublattices. Trim lattices satisfy a weakened form of modularity. The order complex of a trim lattice is contractible or homotopic to a sphere; the latter holds exactly if the maximum element of the lattice is a join of atoms. Any distributive lattice is trim, but trim lattices need not be graded. The main example of ungraded trim lattices are the Tamari lattices and generalizations of them. We show that the Cambrian lattices in types A and B defined by Reading are trim; we conjecture that all Cambrian lattices are trim. 相似文献
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O. A. Kuryleva 《Algebra and Logic》2008,47(1):42-48
A vector space V over a real field R is a lattice under some partial order, which is referred to as a vector lattice if u + (v ∨ w) = (u + v) ∨ (u + w) and u
+ (v ∧ w) = (u + v) ∧ (u + w) for all u, v, w ∈ V. It is proved that a model N of positive integers with addition and multiplications is relatively elementarily interpreted in the ideal lattice
ℱ
n
of a free vector lattice ℱ
n
on a set of n generators. This, in view of the fact that an elementary theory for N is hereditarily undecidable, implies that an elementary theory for
ℱ
n
is also hereditarily undecidable.
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Translated from Algebra i Logika, Vol. 47, No. 1, pp. 71–82, January–February, 2008. 相似文献
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明平华 《数学的实践与认识》2004,34(6):159-161
由幂格的定义知 ,幂格与幂集格是不同的 ,然而它们却有一定的联系 .本文在幂格概念的基础上 ,进一步地讨论幂格和幂集格在一定条件下的联系 . 相似文献
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幂格的同态与同余关系 总被引:1,自引:1,他引:0
本文在文[1]已引入幂格同态概念的基础上,进一步引入幂格同余关系的概念,并得到它们的一些相关性质.以及幂格同态与幂格同余关系的对应关系. 相似文献
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M. V. Semenova 《Algebra and Logic》2006,45(2):124-133
V. B. Repnitskii showed that any lattice embeds in some subsemilattice lattice. In his proof, use was made of a result by
D. Bredikhin and B. Schein, stating that any lattice embeds in the suborder lattice of a suitable partial order. We present
a direct proof of Repnitskii’s result, which is independent of Bredikhin—Schein’s, giving the answer to a question posed by
L. N. Shevrin and A. J. Ovsyannikov. We also show that a finite lattice is lower bounded iff it is isomorphic to the lattice
of subsemilattices of a finite semilattice that are closed under a distributive quasiorder.
Supported by INTAS grant No. 03-51-4110; RF Ministry of Education grant No. E02-1.0-32; Council for Grants (under RF President)
and State Aid of Fundamental Science Schools, project NSh-2112.2003.1; a grant from the Russian Science Support Foundation;
SB RAS Young Researchers Support project No. 11.
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Translated from Algebra i Logika, Vol. 45, No. 2, pp. 215–230, March–April, 2006. 相似文献