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Proceedings of the American Mathematical Society
Proceedings of the American Mathematical Society
ISSN 1088-6826(online) ISSN 0002-9939(print)

 

Ranks of matrices over Ore domains


Authors: H. Bedoya and J. Lewin
Journal: Proc. Amer. Math. Soc. 62 (1977), 233-236
MSC: Primary 16A06
MathSciNet review: 0437573
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Abstract | References | Similar Articles | Additional Information

Abstract: Let R be a Noetherian Ore domain. Then rank M = inner rank M for every matrix M over R if and only if R is projective-free of global dimension at most 2.


References [Enhancements On Off] (What's this?)

  • [1] G. Bergman, Commuting elements in free algebras and related topics in ring theory, Thesis, Harvard University, 1967.
  • [2] K. W. Gruenberg, Cohomological topics in group theory, Lecture Notes in Math., vol. 143, Springer-Verlag, Berlin and New York, 1970. MR 43 #4923. MR 0279200 (43:4923)
  • [3] I. Kaplansky, Fields and rings, 2nd ed., Chicago Notes in Math., Univ. of Chicago Press, Chicago, Ill., 1972. MR 0349646 (50:2139)
  • [4] D. Lissner and A. Geramita, Remarks on OP and Towber rings, Canad. J. Math. 22 (1970), 1109-1117. MR 42 #5972. MR 0271089 (42:5972)

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Additional Information

DOI: http://dx.doi.org/10.1090/S0002-9939-1977-0437573-6
PII: S 0002-9939(1977)0437573-6
Keywords: Rank of matrices, Ore domain
Article copyright: © Copyright 1977 American Mathematical Society