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Some classes of semi-perfect rings

Grant number: 12/00878-3
Support type:Research Grants - Visiting Researcher Grant - International
Duration: July 04, 2012 - November 03, 2012
Field of knowledge:Physical Sciences and Mathematics - Mathematics - Algebra
Principal researcher:Mikhailo Dokuchaev
Grantee:Mikhailo Dokuchaev
Visiting researcher: Volodymyr Kyrychenko
Visiting researcher institution: Taras Shevchenko National University of Kyiv, Ukraine
Home Institution: Instituto de Matemática e Estatística (IME). Universidade de São Paulo (USP). São Paulo , SP, Brazil
Associated research grant:09/52665-0 - Groups, rings and algebras: interactions and applications, AP.TEM

Abstract

During the visit of Professor Vladimir Kirichenko we are going to study relevant classes of semi-perfect rings, such as semi-perfect rings which are semi-distributive, tiled orders and serial rings. In particular, we shall consider semi-perfect semi-distributive rings whose local rings are discrete valuation rings or uniserial rings. We shall also investigate the relation between serial rings and Frobenius rings, the two-sided ideals in semi-perfect semi-distributive rings, as well as groups of units in tiled rings, serial rings and other classes of semi-perfect rings. (AU)