Algebraický seminář
Ela Celikbas (West Virginia Univ.): Full-Trace Modules over Local Rings
Olgur Celikbas (West Virginia Univ.): TBA
Abstract: (Ela Celikbas): A module over a commutative Noetherian local ring carries information about the ring through the maps it admits back into the ring. The images of all such maps generate an ideal, called the trace of the module. In this talk, I will discuss modules whose trace is the maximal ideal; in this sense, they detect as much of the ring as possible without detecting the whole ring. We call these full-trace modules. The main focus of the talk will be on syzygy modules of the residue field. I will explain when these syzygies are full-trace and how the answer reflects the structure of the underlying ring. I will also discuss the interaction between full-trace modules and Ulrich modules, showing in particular that the existence of a full-trace Ulrich module characterizes non-regular Cohen–Macaulay local rings of minimal multiplicity. This is joint work with Olgur Celikbas, Jürgen Herzog, and Shinya Kumashiro.
Abstract (Olgur Celikbas): .
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.
