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Proceedings of the American Mathematical Society

ISSN 1088-6826(online) ISSN 0002-9939(print)

 
 

 

A singular primitive ring


Author: John Lawrence
Journal: Proc. Amer. Math. Soc. 45 (1974), 59-62
MSC: Primary 16A20
DOI: https://doi.org/10.1090/S0002-9939-1974-0357466-X
MathSciNet review: 0357466
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Abstract: An example of a primitive ring with nonzero singular ideal is constructed. An example, due to B. Osofsky, of a semiprimitive ring with nonzero singular ideal is shown to be nonprimitive.


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

  • [1] C. Faith, Lectures in injective modules and quotient rings, Lecture Notes in Math., no. 49, Springer-Verlag, Berlin and New York, 1967. MR 37 #2791. MR 0227206 (37:2791)
  • [2] E. Formanek, Group rings of free products are primitive, J. Algebra 26 (1973), 508-511. MR 0321964 (48:329)
  • [3] B. Osofsky, A non-trivial ring with non-rational injective hull, Canad. Math. Bull. 10 (1967), 275-282. MR 35 #2930. MR 0212055 (35:2930)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1974-0357466-X
Keywords: Primitive ring, singular ring, singular ideal, semiprimitive ring
Article copyright: © Copyright 1974 American Mathematical Society

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