Study on elucidation of Algebratc Structure of rings applying Representation Theories of Finite dimerstcrra algebhas, Griupalgerhras and Lie Alberas

我们在1997年举办了第30届环理论和表示论研讨会（10月20日至23日，长野，信州大学），我们邀请了来自加拿大卡尔顿大学的V.DIAB教授，这些成果发表在第30届Ring Theory and Representation Theory Symposium论文集上，从Lie环的角度研究了群环，结合方案的研究.我们还用同调方法研究了自反模，这与表示论密切相关.我们参加了许多学术会议来介绍我们的结果，并通过参加相关会议获得了很多信息. 1998年，我们参加了在德国的比勒费尔德举行的代数表示论国际会议，介绍了我们的结果。此外，我们访问了捷克布拉格的查尔斯大学，会见了V.DIAB教授（他也是加拿大卡尔顿大学的教授，我们在1997年通过该基金邀请了他）。他回顾了我们的研究成果。我们邀请了筑波大学的星野教授，以了解对今后研究环论很重要的导出范畴的信息。与1997年一样，我们继续积极参加许多会议，以促进我们的研究。通过使用范畴方法，在表示论中，我们可以比Morita等价或环同构更广泛地分类，并且我们找到了发展我们的方法来描述更确切地说，是环之间的内在联系。

We held the 30th Ring Theory and Representation Theory Symposium in 1997(October 20-23, Nagano, Shinshu-University) and we invited Professor V.DIab from Carleton University in Canada, who has been studying what was closely related to our study.These achievement was published to Proceeding of the 30th Ring Theory and Representation Theory Symposium.Group rings was studied in the stand point of view of Lie ring and association scheme in addition to the ring theoretical point of view.Also we studied about reflexive modules by using homological method, which is closely related to the representation theory.We attended to many academic meetings to present our results and we get much information by attending related meetings.In 1998, we attended to the International Conference of the RepresentationTheory of Algebra held at Bielefeld in Germany to present our results.In addition, e visited Charles University in Plague in Czech to meet to Professor V.DIab (who is also Professor of Carleton University in Canada and we invited him in 1997 by this fund). He reviewed our results.We invited Professor Hoshino from Tsukuba University to get information about Derived Category which seems to be important to study ring theory from now.Same as 1997, we continued to attend many meetings aggressively to promote our study.By using categorical method, in representation theory we can classify more wideIy than Morita equivalence or ring isomorphism and we found the way to develop our method for describing more precisely the internal relations between rings.