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Proceedings of the American Mathematical Society

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

 
 

 

Quotient full linear rings


Author: John J. Hutchinson
Journal: Proc. Amer. Math. Soc. 28 (1971), 375-378
MSC: Primary 16A42
DOI: https://doi.org/10.1090/S0002-9939-1971-0424867-8
MathSciNet review: 0424867
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Abstract: We define a ring $ R$ to be an FL (full linear) ring if $ R$ is isomorphic to the full ring of linear transformations of a left vector space over a division ring. $ R$ is QFL if its left maximal quotient ring is an FL ring. In this paper we give necessary and sufficient conditions for a ring to be a QFL ring. We also generalize some results of Chase and Faith concerning subdirect sum decompositions of rings whose left maximal quotient ring is the direct product of FL rings.


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

  • [1] S. U. Chase and C. Faith, Quotient rings and direct products of full linear rings, Math. Z. 88 (1965), 250-264. MR 31 #2281. MR 0178023 (31:2281)
  • [2] C. Faith, Lectures on injective modules and quotient rings, Lecture Notes in Math., no. 49, Springer-Verlag, New York, 1967. MR 37 #2791. MR 0227206 (37:2791)
  • [3] J. Hutchinson, Essential subdirect sums of rings (to appear).

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1971-0424867-8
Keywords: Maximal quotient ring, complete quotient ring, classical quotient ring, full linear ring, essential extension, subdirect sums
Article copyright: © Copyright 1971 American Mathematical Society

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