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arXiv · 1311.5741

The commutant of simple modules over almost commutative algebras

Oliver Ungermann
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Abstract

Let $B$ be a finitely generated algebra over a field $k$. Then $B$ is called a Jacobson algebra if every semiprime ideal of $B$ is semiprimitive. We will discuss several conditions, all involving the commutant of simple $B$-modules, which imply that $B$ is Jacobson. In particular, we will recover the well-known result that every finitely generated almost commutative algebra is Jacobson. The same holds true for $\mathbb{N}$-filtered $k$-algebras $B$ with a locally finite filtration such that the associated graded $k$-algebra is left-noetherian.

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Oliver Ungermann. 2013-11-22. The commutant of simple modules over almost commutative algebras. https://arxiv.org/abs/1311.5741

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