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October 2006 Factorization in Quantum Planes
Romain Coulibaly, Kenneth Price
Missouri J. Math. Sci. 18(3): 197-205 (October 2006). DOI: 10.35834/2006/1803197

Abstract

These results stem from a course on ring theory. Quantum planes are rings in two variables $x$ and $y$ such that $yx=qxy$ where $q$ is a nonzero constant. When $q=1$, a quantum plane is simply a commutative polynomial ring in two variables. Otherwise, a quantum plane is a noncommutative ring.

Our main interest is in quadratic forms belonging to a quantum plane. We provide necessary and sufficient conditions for quadratic forms to be irreducible. We find prime quadratic forms and consider more general polynomials. Every prime polynomial is irreducible and either central or a scalar multiple of $x$ or of $y$. Thus, there can only be primes of degree 2 or more when $q$ is a root of unity.

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Romain Coulibaly. Kenneth Price. "Factorization in Quantum Planes." Missouri J. Math. Sci. 18 (3) 197 - 205, October 2006. https://doi.org/10.35834/2006/1803197

Information

Published: October 2006
First available in Project Euclid: 3 August 2019

zbMATH: 1181.16028
Digital Object Identifier: 10.35834/2006/1803197

Subjects:
Primary: 16W35
Secondary: 81R50

Rights: Copyright © 2006 Central Missouri State University, Department of Mathematics and Computer Science

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Vol.18 • No. 3 • October 2006
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