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Non-isomorphic rings with isomorphic matrix rings

Published online by Cambridge University Press:  20 January 2009

A. W. Chatters
Affiliation:
School of Mathematics, University Walk, Bristol BS8 1TW
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Abstract

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We construct an uncountable family of pairwise non-isomorphic rings Si, such that the corresponding full 2 by 2 matrix rings M2(Si) are all isomorphic to each other. The rings Si are Noetherian integral domains which are finitely-generated as modules over their centres.

Type
Research Article
Copyright
Copyright © Edinburgh Mathematical Society 1993

References

REFERENCES

1.Chatters, A. W. and Hajarnavis, C. R., Rings with chain conditions (Pitman, London, 1980).Google Scholar
2.Chatters, A. W., Matrices, idealisers, and integer quaternions, J. Algebra, 150 (1992), 4556.CrossRefGoogle Scholar
3.Letzter, G. and Makar-Limanov, L., Rings of differential operators over rational affine curves, Bull. Soc. Math. France, to appear.Google Scholar
4.Levy, L. S., Robson, J. C. and Stafford, J. T., Hidden matrices, in preparation.Google Scholar
5.McConnell, J. C. and Robson, J. C., Non-commutative Noetherian rings (Wiley, 1987).Google Scholar
6.Smith, S. P., An example of a ring Morita-equivalent to the Weyl algebra A 1 J. Algebra 73 (1981), 552555.CrossRefGoogle Scholar
7.Stafford, J. T., Endomorphisms of right ideals of the Weyl algebra, Trans. Amer. Math. Soc. 299 (1987), 623639.CrossRefGoogle Scholar