Graduation Term
2022
Degree Name
Master of Science (MS)
Department
Department of Mathematics
Committee Chair
Wenhua Zhao
Abstract
In 2010, W. Zhao introduced the notion of a Mathieu subspace as a common framework for study of the Jacobian conjecture and related topics. As a generalization of ideals, Mathieu subspaces provide a new viewpoint to investigate the structure of associative algebras and rings. In this paper, we classify Mathieu subspaces of the Burnside algebras $\mathscr{B}_k(G)$ and $\mathscr{B}_k(D_{2p})$ where $k$ is a field of characteristic $p > 0$, $G = H \times K$ for a $p$-group $H$ and a $p'$-group $K$, and $D_{2p}$ is the dihedral group of order $2p$ (for $p$ odd).
Access Type
Thesis-Open Access
Recommended Citation
Hatfield, Andrew Burak, "Mathieu-Zhao Subspaces of Burnside Algebras of some Finite Groups" (2022). Theses and Dissertations. 1601.
https://ir.library.illinoisstate.edu/etd/1601
DOI
https://doi.org/10.30707/ETD2022.20221020070311922675.999987
