Algebraický seminář
Leonid Positselski (IM CAS Prague): Relatively left perfect homomorphisms of rings
Abstract: An associative ring R is left perfect if and only if all left R-modules are cotorsion. Given a ring homomorphism R --> A, one can easily see that any cotorsion A-module is also cotorsion as an R-module. A homomorphism of associative rings R --> A is said to be relatively left perfect if every left A-module that is cotorsion over R is also cotorsion over A. Equivalently, this means that every flat left A-module is A/R-flaprojective, i.e., a direct summand of an A-module filtered by the A-modules A \otimes_R G, where G ranges over flat left R-modules. In this talk I will prove that the ring homomorphism R --> A is relatively left perfect whenever A is a finitely generated projective right R-module.
October 20 - TBA
The Algebra Seminar was founded by Vladimir Korinek in the early 1950's and continued by Karel Drbohlav until 1981. The seminar resumed its activities in 1990 under the guidance of Jaroslav Jezek and Tomas Kepka. Since 1994, the seminar is headed by Jan Trlifaj.
Presently, the seminar is supported by GACR. It serves primarily as a platform for presentation of recent research of the visitors to the Department of Algebra as well as members of the Department and their students.
