Representations of regular*-semigroups and their application to partial symmetry

正则*-半群的表示及其在部分对称性中的应用

• 批准号: 17540025
• 负责人: IMAOKA Teruo
• 金额: $ 1.84万
• 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: 2005
• 资助国家: 日本
• 起止时间: 2005 至 2007
• 项目状态: 已结题
• 来源: https://kaken.nii.ac.jp/grant/KAKENHI-PROJECT-17540025/
• 关键词: algebra; *-semigroup; regular semigroup; renresentation; argorithm; geometry; topology; partial symmetry; 半群; 正則*半群; 表現論

The purpose of this research is to study the representations of regular *-semigroups and their application to partial symmetry. During the term of our project, the head investigator obtained the following. For the results of other investigators and their detail, see the references in the larar.1. By introducing the concept "biarrowed word tree", we obtained that the free generalized inverse *-semigroup is isomorphic to the set of all biarrowed word tree in respect to the new product.2. The category of locally inverse *-semigroups and prehomomorphisms [homomorphisms] is isomorphic to the category of locally inductive *-groupoids and ordered functors [inductive functors].3. By introducing the concept "PG^*-quintet", we constructed a PG^semigroup. And we showed that a generalized inverse *-semigroup S is E-unitary if and only if S is isomorphic to a PG^*-semigroup.4. Any generalized inverse *-semigroup can be embedded in a *-complete, infinitely distributive generalized inverse *-semigroup.5. We characterized a congruence on a generalized inverse *-semigroup by using the concept "*-congruence pair"

本文研究正则 *-半群的表示及其在部分对称性中的应用。在我们的项目期间，首席研究员获得了以下信息。关于其他研究者的结果及其详细信息，请参见larar中的参考文献。通过引入“双箭头词树”的概念，得到了自由广义逆 *-半群同构于关于新积的所有双箭头词树的集合.局部逆 *-半群和预同态范畴同构于局部归纳 *-广群胚和序函子范畴.通过引入PG^*-五重集的概念，构造了一个PG^半群.证明了广义逆 *-半群S是E-酉的当且仅当S同构于PG^*-半群.任何广义逆 *-半群都可以嵌入到 *-完全、无限分配的广义逆 *-半群中。5.利用“*-同余对”的概念刻画了广义逆 *-半群上的同余

项目成果

Some remarks on ordered *-groupoids

关于有序 *-groupoid 的一些评论

• 发表时间: 2005
• 期刊: RIMS Kokyuroku 1437
• 作者: V.A.Chatyrko;Y.Kattori;H.Ohta;T. Imaoka and T. Isobe
• 通讯作者: T. Imaoka and T. Isobe

Representations of generalized inverse *-semigroups

广义逆*-半群的表示

• 发表时间: 2008
• 作者: V.Chatyrko;Y.Hattori;H.Ohta;H. Ohta and T. Imaoka;K. Shoji;H. Ohta and T. Imaoka;H. Ohta and T. Imaoka;H. Ohta and T. Imaoka
• 通讯作者: H. Ohta and T. Imaoka

Algebras, languages, computations and their applications

代数、语言、计算及其应用

• 发表时间: 2007
• 作者: Y. Hattori;H. Tsuiki;K. Shoji
• 通讯作者: K. Shoji

「代数, 形式言語, 計算システム理論とその応用」数理解析研究所講究録1562巻

《代数、形式语言、计算系统理论及其应用》数学分析研究所 1562 卷

• 发表时间: 2007
• 作者: Y. Hattori;H. Tsuiki;K. Shoji;庄司邦孝
• 通讯作者: 庄司邦孝

Lawson topology of the space of formal balls and hyperbolic topology

形式球空间的劳森拓扑和双曲拓扑

• 发表时间: 2008
• 期刊: heoret. Comput. Sci 405
• 作者: S. Dolecki;H. Kunzi & T. Nogura;Garcia-Ferreira; V. Gutev; T. Nogura;V. Gutev; T. Nogura;V. Gutev; T. Nogura;V. Chatyrko; Y. Hattori;H. Tsiki; Y. Hattori
• 通讯作者: H. Tsiki; Y. Hattori