# A Generalization of Mathieu Subspaces to Modules of Associative Algebras - Mathematics > Representation Theory

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Abstract: We first propose a generalization of the notion of Mathieu subspaces ofassociative algebras $\mathcal A$, which was introduced recently in Z4 andZ6, to $\mathcal A$-modules $\mathcal M$. The newly introduced notion in acertain sense also generalizes the notion of submodules. Related with this newnotion, we also introduce the sets $\sigmaN$ and $\tauN$ of stable elementsand quasi-stable elements, respectively, for all $R$-subspaces $N$ of $\mathcalA$-modules $\mathcal M$, where $R$ is the base ring of $\mathcal A$. We thenprove some general properties of the sets $\sigmaN$ and $\tauN$.Furthermore, examples from certain modules of the quasi-stable algebras Z6,matrix algebras over fields and polynomial algebras are also studied.

Autor: Wenhua Zhao

Fuente: https://arxiv.org/