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1.
In this paper, some classical results of uniquely complemented lattices are extended to uniquely complemented posets (with
0 and 1) like Peirce's Theorem, the Birkhoff–von Neumann Theorem, the Birkhoff–Ward Theorem. Further, it is shown that a section
semi-complemented pseudocomplemented poset is a Boolean poset.
Mathematics Subject Classification (2001) 06A06, 06A11, 06C15, 06C20, 06D15 相似文献
2.
Marcel Erné 《Mathematical Logic Quarterly》2009,55(6):572-586
We compare diverse degrees of compactness and finiteness in Boolean algebras with each other and investigate the influence of weak choice principles. Our arguments rely on a discussion of infinitary distributive laws and generalized prime elements in Boolean algebras. In ZF set theory without choice, a Boolean algebra is Dedekind finite if and only if it satisfies the ascending chain condition. The Denumerable Subset Axiom (DS) implies finiteness of Boolean algebras with compact top, whereas the converse fails in ZF. Moreover, we derive from DS the atomicity of continuous Boolean algebras. Some of the results extend to more general structures like pseudocomplemented semilattices (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim) 相似文献
3.
介绍了双重伪补代数的假值理想和假值同余的概念,并刻画了它们的某些性质.特别地,给出了双重伪补代数的假值理想和假值同余的特征表示. 相似文献
4.
伪补分配格的同余理想与同余关系 总被引:5,自引:1,他引:4
王尊全 《纯粹数学与应用数学》2001,17(4):363-367
L是完备的伪补分配格,I是L的同余理想,本文得到以下结果:⑴θ是L的以I为核的最大同余关系的条件。⑵L的以I为核的同余关系是唯一的充分必要条件。⑶L的同余理想与同余关系之间有一一对应关系的充分必要条件。 相似文献
5.
6.
Sectionally pseudocomplemented semilattices are an extension of relatively pseudocomplemented semilattices—they are meet-semilattices
with a greatest element such that every section, i.e., every principal filter, is a pseudocomplemented semilattice. In the
paper, we give a simple equational characterization of sectionally pseudocomplemented semilattices and then investigate mainly
their congruence kernels which leads to a characterization of subdirectly irreducible sectionally pseudocomplemented semilattices.
Supported by the Council of the Czech Government, MSM 6198959214. 相似文献
7.
在伪补MS-代数上引入余核滤子和完全滤子的概念,研究伪补MS-代数的余核滤子和完全滤子的性质,获得了余核滤子和完全滤子生成的同余关系的表达式,证明了具有余核滤子的最小同余关系有同余一致性. 相似文献
8.
Jie Fang 《数学学报(英文版)》2009,25(6):1031-1040
9.
Josef Niederle 《Order》2001,18(2):161-170
The aim of this paper is to characterize both the pseudocomplemented and Stone ordered sets in a manner similar to that used previously for Boolean and distributive ordered sets. The sublattice G(A) of the Dedekind–Mac Neille completion DM(A) of an ordered set A generated by A is said to be the characteristic lattice of A. We will show that there are distributive pseudocomplemented ordered sets whose characteristic lattices are not pseudocomplemented. We can define a stronger notion of pseudocomplementedness by demanding that both A and G(A) be pseudocomplemented. It turns out that the two concepts are the same for finite and Stone ordered sets. 相似文献
10.
The notion of pseudocomplementedness is weakened in order to obtain a tractable and consistent property of ordered sets, in particular lattices. 相似文献