University Seminar- Computability, Complexity, and Algebraic Structure: Characterizations of semisimple rings in reverse mathematics

Time: Wednesday, May 13, 8:30–9:30pm (evening)

Place: by zoom

https://gwu-edu.zoom.us/j/92667159717

Speaker: Huishan Wu, School of Information Science, Beijing Language and Culture University

Title: Characterizations of semisimple rings in reverse mathematics

Abstract:  The theory of semisimple rings plays a fundamental role in noncommutative algebra. In this talk, we discuss the study of semisimple rings and semisimple modules by methods of reverse mathematics. Semisimple modules are often defined as modules that can be written as direct sums of simple submodules. In 2013, Yamazaki initiated the study of semisimple modules as well as other kinds of modules such as projective modules and injective modules in the context of reverse mathematics. We first consider equivalent characterizations of semisimple modules in reverse mathematics. Then, we define a ring to be left semisimple if the left regular module of it is semisimple and discuss equivalent characterizations of left semisimple rings in reverse mathematics.