# A generalization of Mathieu subspaces to modules of associative algebras

Open Mathematics (2010)

- Volume: 8, Issue: 6, page 1132-1155
- ISSN: 2391-5455

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topWenhua Zhao. "A generalization of Mathieu subspaces to modules of associative algebras." Open Mathematics 8.6 (2010): 1132-1155. <http://eudml.org/doc/269229>.

@article{WenhuaZhao2010,

abstract = {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.},

author = {Wenhua Zhao},

journal = {Open Mathematics},

keywords = {Mathieu subspaces of associative algebras; Mathieu subspaces of modules of associative algebras; (quasi-)stable elements; (quasi-)stable algebras; (quasi-)stable modules; Mathieu subspaces of algebras; Mathieu subspaces of modules; strongly simple algebras; quasi-stable algebras; radicals; idempotents; Jacobian conjecture; matrix algebras; quasi-stable elements; quasi-stable modules},

language = {eng},

number = {6},

pages = {1132-1155},

title = {A generalization of Mathieu subspaces to modules of associative algebras},

url = {http://eudml.org/doc/269229},

volume = {8},

year = {2010},

}

TY - JOUR

AU - Wenhua Zhao

TI - A generalization of Mathieu subspaces to modules of associative algebras

JO - Open Mathematics

PY - 2010

VL - 8

IS - 6

SP - 1132

EP - 1155

AB - 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.

LA - eng

KW - Mathieu subspaces of associative algebras; Mathieu subspaces of modules of associative algebras; (quasi-)stable elements; (quasi-)stable algebras; (quasi-)stable modules; Mathieu subspaces of algebras; Mathieu subspaces of modules; strongly simple algebras; quasi-stable algebras; radicals; idempotents; Jacobian conjecture; matrix algebras; quasi-stable elements; quasi-stable modules

UR - http://eudml.org/doc/269229

ER -

## References

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