A generalization of Mathieu subspaces to modules of associative algebras

• Autorzy: Wenhua Zhao
• Języki publikacji: EN

Abstrakty

EN

We first propose a generalization of the notion of Mathieu subspaces of associative algebras $$ \mathcal{A} $$, 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 $$ \mathcal{A} $$-modules $$ \mathcal{M} $$. 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 $$ \mathcal{A} $$-modules $$ \mathcal{M} $$, where R is the base ring of $$ \mathcal{A} $$. 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.

Słowa kluczowe

EN

Mathieu subspaces of associative algebras; Mathieu subspaces of modules of associative algebras; (quasi-)stable elements; (quasi-)stable algebras; (quasi-)stable modules

Kategorie tematyczne

• 16D10: General module theory
• 16D99: None of the above, but in this section

• Wydawca: De Gruyter Open
• Czasopismo: Open Mathematics
• Rocznik: 2010
• Tom: 8
• Numer: 6
• Strony: 1132-1155

Daty

wydano

2010-12-01

online

2010-10-30

Twórcy

autor

Wenhua Zhao

• Illinois State University

Bibliografia

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• [9] van den Essen A., Wright D., Zhao W., On the image conjecture, preprint available at http://arxiv.org/abs/1008.3962
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• [20] Zhao W., New proofs for the Abhyankar-Gurjar inversion formula and the equivalence of the Jacobian conjecture and the vanishing conjecture, Proc. Amer. Math. Soc. (in press), preprint available at http://arxiv.org/abs/0907.3991
• [21] Zhao W., Mathieu subspaces of associative algebras, preprint available at http://arxiv.org/abs/1005.4260
• [22] Zhao W., Willems R., Analogue of the Duistermaat-van der Kallen theorem for group algebras (in preparation)

Identyfikatory

DOI

10.2478/s11533-010-0068-6