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期刊论文

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2005年04月25日

【期刊论文】Hypersemilattices

赵彬， ZHAO Bin， XIAO Ying， HAN Sheng Wei

，-0001，（）：

-1年11月30日

摘要

In this paper, the hyperstructure will be applied to some aspects of lattice theory. We introduce a series of new concepts, such as hypersemilattice, subhypersemilattice, ideal and so on. And we also study some related properties of them.

hypersemilattice， subhypersemilattice， ideal， hyperorder

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2005年04月25日

【期刊论文】Partially ordered semigroups with the greatest element

赵彬， ZHAO Bin

，-0001，（）：

-1年11月30日

摘要

The purpose of this paper is to discuss some properties of the partially ordered semigroup S containing the greatest element u. We prove that a nontrivial L-class Lu (R-class Ru) is an ideal i

Partially ordered semigroup， Convex ideal， Completely prime ideal， Zero element

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2005年04月25日

【期刊论文】The category of supercontinuous posets

赵彬， ZHAO Bin， ZHOU Yihui

，-0001，（）：

-1年11月30日

摘要

In this paper, we study the order structure-supercontinuous poset, a generalization of completely distributive lattice. The Cartesian product of supercontinuous posets and some other properties of supercontinuous posets are investigated. Also, the case of superalgebraic posets and some categorical properties of supercontinuous posets are studied.

Supercontinuous poset， Super-compact element， Superalgebraic poset， Category

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2005年04月25日

【期刊论文】Lim-inf convergence in partially ordered sets

赵彬， ZHAO Bin ， ZHAO Dongsheng

，-0001，（）：

-1年11月30日

摘要

The lim-inf convergence in a complete lattice was introduced by Scott to characterize continuous lattices. Here we introduce and study the lim-inf convergence in a partially ordered set. The main result is that for a poset P the lim-inf convergence is topological if and only if P is a continuous poset. A weaker form of lim-inf convergence in posets is also discussed.

lim-inf-convergence,， continuous posets,， lim-inf2-convergence,，