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Trace rings of generic matrices are unique factorization domains

Published online by Cambridge University Press:  18 May 2009

Lieven Le Bruyn
Lieven Le Bruyn
Affiliation:
Department of Mathematics, University of Antwerp, UIA Universiteitsplein 1, 2610 Wilrijk, Belgium
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A. W. Chatters and D. A. Jordan defined in [0] a unique factorization ring to be a prime ring in which every height one prime ideal is principal. In this note we will prove that the trace ring of m generic n × n-matrices satisfies this condition.

Throughout this note, k will be a field of characteristic zero. Consider the polynomial ring S = k[;1≤i, j≤n, 1≤l≤m] and the n × n matrices Xl = in Mn(S). The k-subalgebra of Mn(S) generated by {Xl; 1≤l≤m} is called the ring of m generic n × n matrices Gm,n. Adjoining to it the traces of all its elements we obtain the trace ring of m n × n generic matrices, cfr. e.g. [1].

Information

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 28 , Issue 1 , January 1986, pp. 11 - 13
Copyright
Copyright © Glasgow Mathematical Journal Trust 1986

References

REFERENCES

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