A generalization of Mathieu subspaces to modules of associative algebras

Wenhua Zhao

Open Mathematics, Tome 8 (2010), p. 1132-1155 / Harvested from The Polish Digital Mathematics Library

Résumé

We first propose a generalization of the notion of Mathieu subspaces of associative algebras 𝒜 , which was introduced recently in [Zhao W., Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra, 2010, 214(7), 1200–1216] and [Zhao W., Mathieu subspaces of associative algebras], to 𝒜 -modules ℳ . The newly introduced notion in a certain sense also generalizes the notion of submodules. Related with this new notion, we also introduce the sets σ(N) and τ(N) of stable elements and quasi-stable elements, respectively, for all R-subspaces N of 𝒜 -modules ℳ , where R is the base ring of 𝒜 . We then prove some general properties of the sets σ(N) and τ(N). Furthermore, examples from certain modules of the quasi-stable algebras [Zhao W., Mathieu subspaces of associative algebras], matrix algebras over fields and polynomial algebras are also studied.

Détail

Publié le : 2010-01-01

Zbl 1256.16013

EUDML-ID : urn:eudml:doc:269229

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