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Filtrations in semisimple rings
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In this paper, we describe the maximal bounded
Z
\mathbb {Z}
-filtrations of Artinian semisimple rings. These turn out to be the filtrations associated to finite
Z
\mathbb {Z}
-gradings. We also consider simple Artinian rings with involution, in characteristic
≠
2
\neq 2
, and we determine those bounded
Z
\mathbb {Z}
-filtrations that are maximal subject to being stable under the action of the involution. Finally, we briefly discuss the analogous questions for filtrations with respect to other Archimedean ordered groups.
American Mathematical Society (AMS)
Title: Filtrations in semisimple rings
Description:
In this paper, we describe the maximal bounded
Z
\mathbb {Z}
-filtrations of Artinian semisimple rings.
These turn out to be the filtrations associated to finite
Z
\mathbb {Z}
-gradings.
We also consider simple Artinian rings with involution, in characteristic
≠
2
\neq 2
, and we determine those bounded
Z
\mathbb {Z}
-filtrations that are maximal subject to being stable under the action of the involution.
Finally, we briefly discuss the analogous questions for filtrations with respect to other Archimedean ordered groups.
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