Combinatorial semigroup theory and its applications

（1）群的归并问题与群的文字问题密切相关，特别是通过群的归并积。从而解决了许多群体的文字问题，利用群体的融合产品取得了良好的效果。然而，说半群的情况完全改变也不过分。事实上，群体的混合体总是可以嵌入到群体中。但半群的混合并不总是可嵌入半群中。M.Sapir否定地证明了半群的归并问题，提出了“是否存在一个算法来判定有限半群的归并是否可嵌入有限半群中”的问题。此外，M.Sapir和T. E. Hall研究了“是否存在一个算法来决定一个有限半群是否是所有半群的合并基”的可判定性问题。然而，它仍然没有解决。通过对这个问题的研究，我们得到了Okninski和Putch的另一个证明 ...更多信息 有限逆半群的A定理进一步给出了正则半群是所有半群的合并基的一个充分条件。（2）从拓扑学的角度，构造了连续映射的纤维同伦群框架，研究了可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-演算的重写系统和平移。从效用计算建模的角度，证明了自由λμ-演算的外建模的存在性，研究了自由λ μ-演算的融合性以及自由λμ-演算与C-幺半群的关系.从代数算法的角度研究了以中心有限维单Artin环为商环的Dubrovin赋值环的R-理想。为了阐明Iwasawa模与Galois群计算的关系，研究了Z_p-扩张与Galois群的关系，得到了Iwasawa定理的一个推广和Greenberg猜想的一些结果.少

(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