权益分类	功能权益	普通用户	{{item.name}}会员
{{category.name}}	{{benefitItem.name}}

Combinatorial semigroup theory and its applications

组合半群理论及其应用

基本信息

批准号：
15540029
负责人：
SHOJI Kunitaka
金额：
$ 2.37万
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：
2003
资助国家：
日本
起止时间：
2003 至 2004
项目状态：
已结题

项目摘要

(1)Amalgamation problems for groups are strongly connected with word problems for groups, Especially, through amalgamation products of groups。 Consequently, many word problems for groups have been solved and many nice results have been brought by making use of amalgamation products of groups。However, it is not too much to say that the situation for semigroups changes totally。 Actually, amalgams of groups are always embeddable in a group。 But amalgams of semigroups are not always embeddable in a semigroup。 M.Sapir proved negatively the amalgamation problem of semigroups asking fo "Does there exist an algorithm to decide whether or not an amalgam of finite semigroups are embeddable in a finite semigroup"。 Moreover、M.Sapir and T.E.Hall study the decidability pr@blem of "Does there exist an algorithm to decide whether or not a finite semigroup is an amalgamation base for all the semigroups. However, it is left unsolved. Investing the problem, we obtained another proof of Okninski and Putch … More a's theorem for finite inverse semigroups. Furthermore、we give a sufficient condition for regular semigorups to be an amalgamation base for all the semigroups.(2)From a point view of topology, we construct frame work of fiber homotopy groups of continuous mapping and study fibre ANR property of mappings between stratifirable spaces(3)From a point view of mathematical logic, we investigate rewriting systems and translations of λμ-calculus. From a point view of Utility computation modeling, we show the existence of exterior modeling for free λμ-calculus and study confluence of free λμ-calculus and relationship between free λμ-calculus and C-monoids. From a point view of algebraic algorithm, we study R-ideals of Dubrovin valuation rings with central finite dimensional Simple Artinian ring as a quotient ring. To clarify relationship between Iwasawa modules and computations of Galois groups, we investigate relationship between Z_p-extensions and Galois groups and obtain a generalization of Iwasawa theorem and some results on Greenberg's conjecture. Less

(1)群的合并问题与群的应用问题密切相关，特别是通过群的合并乘积。因此，许多群的应用问题已经被解决，并且通过利用群的合并乘积带来了许多好的结果。但是，可以说半群的情况完全改变了。实际上，群的合并总是可嵌入到一个群中的。但是半群并不总是可嵌入半群中。M.Sapir 反证了半群的合并问题，询问“是否存在一种算法来决定有限半群的混合是否可嵌入有限半群中”。此外，M.Sapir 和 T.E.Hall 研究了“是否存在一种算法”的可判定性问题决定有限半群是否是所有半群的合并基。然而，它仍然悬而未决。通过研究这个问题，我们得到了 Okninski 和 Putch … More a 有限逆半群定理的另一个证明。此外，我们还给出了正则半群成为所有半群的合并基的充分条件。(2)从拓扑结构，构建了连续映射的纤维同伦群框架，研究了可分层空间之间映射的纤维ANR性质。(3)从数理逻辑的角度，研究了λμ微积分的重写系统和翻译。从效用计算建模的角度出发，证明了自由λμ演算的外部建模的存在性，并研究了自由λμ演算的融合。以及自由 λμ-演算和 C-幺半群之间的关系。从代数算法的角度出发，研究了以中心有限维Simple Artinian环为商环的杜布罗文估价环的R理想。为了阐明 Iwasawa 模和 Galois 群计算之间的关系，我们研究了 Z_p-extensions 和 Galois 群之间的关系，并得到了岩泽定理和格林伯格猜想的一些结果。少