Geodesic
Trace rings of generic matrices are unique factorization domains
Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 11-13

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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]. 
Bruyn, Lieven Le. Trace rings of generic matrices are unique factorization domains. Glasgow mathematical journal, Tome 28 (1986) no. 1, pp. 11-13. doi: 10.1017/S0017089500006261
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[0] 0.Chatters, A. W. and Jordan, D. A., Non-commutative unique factorization rings, preprint. Google Scholar

[1] 1.Amitsur, S. A. and Small, Lance W., Prime Ideals in p.i. Rings, J. Algebra 62 (1980), 358–383. Google Scholar | DOI

[2] 2.Artin, Emil, Letter dated 12 3rd, 1982. Google Scholar

[3] 3.Auslander, Maurice and Goldman, Oscar, Maximal Orders, Trans. Amer. Math. Soc. 97 (1960), 1–24. Google Scholar | DOI

[4] 4.Fossum, Robert M., The Divisor Class Group of a Krull Domain, Ergebn. der Math. Wiss. 74 (Springer Verlag, 1973). Google Scholar | DOI

[5] 5.Bruyn, Lieven Le, Homological Properties of Trace Rings of Generic Matrices, Trans. Amer. Math. Soc. (to appear). Google Scholar

[6] 6.Procesi, Claudio, Invariant Theory of n × n Matrices, Advances in Math. (1976). Google Scholar | DOI

[7] 7.Small, Lance W. and Stafford, J. T., Holological Properties of Generic Matrices, Israel J. Math., (to appear). Google Scholar

[8] 8.Yuan, Shuen, Reflexive Modules and Algebra Class Groups over Noetherian Integrally Closed Domains, J. Algebra 32 (1974), 405–417. Google Scholar | DOI

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