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Published online by Cambridge University Press:  01 September 2007

Department of Mathematics and Statistics, University of Otago, PO Box 56, Dunedin, New Zealand e-mail:
Department of Mathematics, Ohio University, Athens, Ohio 45701, USA e-mail:
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Using a variation on the concept of a CS module, we describe exactly when a simple ring is isomorphic to a ring of matrices over a Bézout domain. Our techniques are then applied to characterise simple rings which are right and left Goldie, right and left semihereditary.

Research Article
Copyright © Glasgow Mathematical Journal Trust 2007



1.Anderson, F. W. and Fuller, K. R., Rings and categories of modules, Second edition (Springer-Verlag, 1992).Google Scholar
2.Camillo, V. P. and Cozzens, J., A theorem on Noetherian hereditary rings, Pacific J. Math. 45 (1973), 3541.Google Scholar
3.Chatters, A. W. and Hajarnavis, C. R., Rings in which every complement right ideal is a direct summand, Quart. J. Math. Oxford Ser. (2) 28 (1977), 6180.Google Scholar
4.Clark, J. and Wisbauer, R., Σ-extending modules, J. Pure Appl. Algebra 104 (1995), 1932.Google Scholar
5.Cohn, P. M., Free rings and their relations, Second edition (Academic Press, 1985).Google Scholar
6.Cohn, P. M., Right principal Bezout domains, J. London Math. Soc. (2) 35 (1987), 251262.Google Scholar
7.Cohn, P. M. and Schofield, A. H., Two examples of principal ideal domains, Bull. London Math. Soc. 2 (1985), 2528.Google Scholar
8.Cozzens, J. and Faith, C., Simple Noetherian rings (Cambridge Univ. Press, 1975).Google Scholar
9.Dung, N. V., Huynh, D. V., Smith, P. F. and Wisbauer, R., Extending modules (Longman Scientific & Technical, Harlow, 1994).Google Scholar
10.Goodearl, K. R., Von Neumann regular rings, Second Edition (Krieger Publishing Company, Malabar, 1991).Google Scholar
11.Hanada, K., Kuratomi, Y. and Oshiro, K., On direct sums of extending modules and internal exchange property, J. Algebra 250 (2002), 115133.Google Scholar
12.Hart, R., Simple rings with uniform right ideals, J. London Math. Soc. 42 (1967), 614617.Google Scholar
13.Huynh, D. V., Jain, S. K. and López-Permouth, S. R., On the symmetry of the Goldie and CS conditions for prime rings, Proc. Amer. Math. Soc. 128 (2000), 31533157.Google Scholar
14.Huynh, D. V., Jain, S. K. and López-Permouth, S. R., Prime Goldie rings of uniform dimension at least two and with all one-sided ideals CS are semihereditary, Comm. Algebra 31 (2003), 53555360.Google Scholar
15.Mc Connell, J. C. and Robson, J. C., Noncommutative noetherian rings (Wiley, 1987).Google Scholar
16.Mohamed, S. H. and Müller, B. J., Continuous and discrete modules (Cambridge University. Press, 1990).Google Scholar
17.Small, L. W., Semihereditary rings, Bull. Amer. Math. Soc. 73 (1967), 656658.Google Scholar