双重Stone代数的主同余关系

给出了双重Stone代数的主同余关系θ(a,b)(a≤b)的等式刻划以及其它的一些性质,由此得到了主同余关系θ(a,b)(a≤b)存在Boo le-补的若干充分条件.     

二项式系数幂和序列在模p2下的几个性质

利用同余理论和多项式理论研究二项式系数幂和序列在模p2下的同余性质,得到了一些非平凡结果.为进一步研究二项式系数幂和序列的多项式递推公式提供有利的工具.     

一个求解二项式系数幂和序列递推公式的方法

根据同余理论并利用二项式系数幂和序列在模p下具有周期性的事实,提出一种求解递推公式的方法,从理论上证明其可行性.使得求解和验证二项式系数幂和序列递推公式具有完备的理论基础.     

On subnormal subgroups of linear groups

We describe the subnormal subgroups of 2-dimensional linear groups over local and full rings in which 2 is invertible, as well as the subnormal subgroups of symplectic groups over local rings in which 2 is invertible.     

On congruences and ideals of partially ordered quasigroups

Some results concerning congruence relations on partially ordered quasigroups (especially, Riesz quasigroups) and ideals of partially ordered loops are presented. These results generalize the assertions which were proved by Fuchs in [5] for partially ordered groups and Riesz groups.     

Representations of distributive semilattices in ideal lattices of various algebraic structures

We study the relationships among existing results about representations of distributive semilattices by ideals in dimension groups, von Neumann regular rings, C*-algebras, and complemented modular lattices. We prove additional representation results which exhibit further connections with the scattered literature on these different topics. Received March 2, 1998; accepted in final form November 9, 2000.     

《数书九章》大衍类算题中的数论命题

《数书九章》是我国著名数学家南宋秦九韶撰写(公元1247年)。青年时他“侍亲中都(临安,今杭州市)因得访习于太史(国家天文历法官员)”。《数书九章》有“大衍总数术”以处理天文历法问题,系统论述同余式解法,这在我国历史上是第一次,在世界数学史上也是创举。 本文用整数论知识来检验《数书九章》中有关解同余式算题(大衍类)题文、术文、草文以及清代学者所作注文的得失,使对我国传统数学在这一领域内的工作有,较系统的认识。     

一类循环系的平坦性

设Ｓ是幺半群,ｘ_１,ｘ₂,…∈Ｓ且满足ｘ_i+１ｘ_i＝ｘ_i,ｉ＝１,２……ｙ是S中的任意元素,记H={(yx_i,x_i)|i=1,2,…}.设ρ(H)是S的由Ｈ生成的最小右同余,本文证明了S／ρ（Ｈ）是平坦右Ｓ－系．