Algebraický seminář
Pietro Freni (IM CAS): Generalized power series and strong vector spaces
Abstract: Rings and fields of series with well-ordered (or well-partially ordered) support are relevant to some parts of the theories of valued fields, o-minimal structures, and asymptotic analysis. A central notion in applications to the latter two subjects is that of formal summability. This recently prompted the development of a suitable notion of vector space with a "notion of formal summability and infinite sums", resulting in the notions of strong vector space and ultrafinite summability space, which although independently defined, turned out to be equivalent.
After giving a brief overview of the motivation, I will survey on these notions covering some basic facts such as the relation of strong vector spaces with linearly topologized vector spaces. In the last part I will discuss a natural question arising in this context that might need set-theoretic tools for to be answered.
March 16 - Tsutomu Nakamura (Kyoto University of Education)
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.
