Event Details
Algebra seminar
Speaker: Tamar Mesablishvili ( Universidad de Granada)
Abstract: Factorizations of mathematical objects is an important topic in Mathematics. The factorization problem consists of both finding all the factorizations of a given mathematical object through its subobjects, and studying properties of a mathematical objects in terms of the two smaller subobjects through which it is already factorized. It occurs frequently that it is possible to solve the initial problem for these subobjects, for which one has techniques that weren’t available for the initial object. Therefore, the factorization problem is crucial and it is being studied and researched in many different fields of Mathematics. Our goal was to describe the set of all possible factorizations of a given monoid. Two necessary and sufficient conditions in terms of so-called descent 1-cocyles for a monoid to be factorized through two submonoids were found. A full classification of those factorizations of a monoid whose one factor is a subgroup of the monoid was obtained.
