COMBINATORIAL SEMIGROUP THEORY AND ITS APPLICATIONS

组合半群理论及其应用

基本信息

批准号：
09640038
负责人：
UEDA Akira
金额：
$ 1.98万
依托单位：
SHIMANE UNIVERSITY
依托单位国家：
日本
项目类别：
Grant-in-Aid for Scientific Research (C)
财政年份：
1997
资助国家：
日本
起止时间：
1997 至 1998
项目状态：
已结题

项目摘要

1. Decision problem whether or not a finite semigroup has a certain property (P) has been studied by many mathematicians, and Spair and Guba proved that for many properties (P) the decision problem is undecidable. Concerning this problem, Shoji proved that there exists an algorithm to decide whether or not a finite semigroup has the representation extension property. Furthermore, shoji proved the following results(1) For completely 0-simple semigroup S, the following are equivalent.(i) S is a special amalgamation base.(ii) S is either left absolutely flat or right absolutely flat.(iii) S satisfies either left annihilator condition or right annihilator condition.(2) For finite commutative semigroup T, the following are equivalent.(i) T is a completely special amalgamation base.(ii) T is completely amalgamation base.(iii) T is E-separable.2. As applications of combinatorial semigroup theory we obtained the following results.(1) Imaoka investigated about representations of generalized inverse *-semigroups.(2) Ueda studied about Prufer orders in simple Artinian rings. In particular, Ueda characterized branched and unbranched prime ideals of Prufer orders.(3) Kondo gave an axiom system of a non-linear 4-valued logic , whose Lindenbaum algebra is the de Morgan algebra with implication.(4) Miwa obtained a new characterization of superparacompact spaces. Miwa also defined new covering properties and studied invariance and inverse invariance under various maps of these covering properties.(5) Kikkawa introduced the algebraic concept of projectivity of a Lie triple algebra and investigated about properties of Lie algebra of projectivity.

1。许多数学家都研究了有限的半群的决策问题，而Spair和Guba证明，对于许多属性（P），决策问题是无法确定的。关于这个问题，Shoji证明存在一种算法来决定有限的半群是否具有表示扩展属性。此外，Shoji证明了以下结果（1）完全简单的半群，以下是等效的。（i）S是一个特殊的合并基础。（ii）S是绝对平坦的或绝对平坦的。（iii）S满足左歼灭剂状态或右边的环境。基础。（ii）t是完全合并的基础。（iii）t是e-2。作为组合半群理论的应用，我们获得了以下结果。（1）Imaoka研究了广义逆 * - 元素的表示形式。（2）UEDA在简单的Artinian Rings中研究了有关Prufer命令的说明。特别是，UEDA表征了Prufer订单的分支和未分支的主要理想。（3）Kondo给出了一个非线性4值逻辑的公理系统，其Lindenbaum代数是de Morgan代数的含义。 Miwa还定义了新的覆盖属性，并研究了这些覆盖属性的各个地图下的不变性和逆不变性。（5）Kikkawa引入了Lie Triple Algebra的预测性代数概念，并研究了投影性的Lie代数的属性。