## Theses and Dissertations

7-1-2022

Thesis

#### Degree Name

Master of Science (MS)

#### Department

Department of Mathematics

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).

Imported from Hatfield_ilstu_0092N_12219.pdf

#### DOI

https://doi.org/10.30707/ETD2022.20221020070311922675.999987

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