Project/Area Number  08640065 
Research Category 
GrantinAid for Scientific Research (C)

Section  一般 
Research Field 
Algebra

Research Institution  Toho University 
Principal Investigator 
KOBAYASHI Yuji Toho University, Faculty of Science, Professor, 理学部, 教授 (70035343)

CoInvestigator(Kenkyūbuntansha) 
UMEZU Yumiko Toho University, Faculty of Medicine, Associate Professor, 医学部, 助教授 (70185065)

Project Fiscal Year 
1996 – 1998

Project Status 
Completed(Fiscal Year 1998)

Budget Amount *help 
¥1,300,000 (Direct Cost : ¥1,300,000)
Fiscal Year 1998 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1997 : ¥400,000 (Direct Cost : ¥400,000)
Fiscal Year 1996 : ¥500,000 (Direct Cost : ¥500,000)

Keywords  algebraic system / finite presentation / word problem / rewriting system / monoid / homotopy / homology / algebraic curve / 代数系 / 有限表示 / 語の問題 / 書換えシステム / モノイド / ホモトピー / 停止性 / 代数曲線 / ホモロジー / 決定問題 / 完備性 / crosssection / 自由モノイド / 正規言語 / 停止問題 
Research Abstract 
We studied the word problem and other decision problems for finitely presented algebras by means of rewriting systems. We found some relationship between the solvability of the word problem and the existence of complete rewriting systems with good properties in a language theoretical sense for finitely presented monoids. We also studied crosssections of monoids related to the above properties. For the word problem to be solvable, contextsensitive crosssections suffice but contextfree crosssections do not (see [2] and [9]). We reported these results in a survey article [5]. We studied some important properties such as confluence and termination of rewriting systems themselves. In [6] we gave a result on the termination for confluent onerule systems. We showed that the rewriting techniques are useful too in the homotopy theory of the derivation graphs associated with monoid presentations. If a monoid has a complete homotopy reduction system, then it satisfies the homological finiteness property FP4. We always have the left canonical reduction system and it is complete if the presentation is nonspecial. These results are reported in [8]. We developed the method to construct a family of algebraic curves of genus g <greater than or equal> 2 with large rank modifying Neron's method
