A Family of Maximal Mathieu Subspaces of Matrix Algebras

arXiv2206.01248MaRDI QIDQ6400969

George F. Seelinger, Wenhua Zhao

Publication date: 2 June 2022

Abstract: Let $F$ be a field. In this note we give a construction for a family of maximal Mathieu subspaces (or Mathieu-Zhao subspaces) of the matrix algebras $M_n(F)$ $(nge2)$. As an application we also give a classification of Mathieu subspaces of $M_2(F)$ under the condition that $F$ is algebraically closed.

Mathematics Subject Classification ID

Finite rings and finite-dimensional associative algebras (16P10) Chain conditions, growth conditions, and other forms of finiteness for associative rings and algebras (16P99) Modules, bimodules and ideals in associative algebras (16D99)

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