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PRIME AND SEMIPRIME QUANTUM LINEAR SPACE SMASH PRODUCTS

Part of: Radicals and radical properties of rings Rings and algebras arising under various constructions

Published online by Cambridge University Press:  23 July 2020

JASON GADDIS
JASON GADDIS*
Affiliation:
Department of Mathematics, Miami University, 301 S. Patterson Ave., Oxford, OH 45056, USA, e-mail: gaddisj@miamioh.edu
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Abstract

Bosonizations of quantum linear spaces are a large class of pointed Hopf algebras that include the Taft algebras and their generalizations. We give conditions for the smash product of an associative algebra with a bosonization of a quantum linear space to be (semi)prime. These are then used to determine (semi)primeness of certain smash products with quantum affine spaces. This extends Bergen’s work on Taft algebras.

MSC classification

Primary: 16S40: Smash products of general Hopf actions
Secondary: 16N60: Prime and semiprime rings
Type
Research Article
Information
Glasgow Mathematical Journal , Volume 63 , Issue 3 , September 2021 , pp. 503 - 514
Copyright
© The Author(s), 2020. Published by Cambridge University Press on behalf of Glasgow Mathematical Journal Trust

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