Quotient full linear rings
Author: John J. Hutchinson
Journal: Proc. Amer. Math. Soc. 28 (1971), 375-378
MSC: Primary 16A42
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.
- Stephen U. Chase and Carl Faith, Quotient rings and direct products of full linear rings, Math. Z. 88 (1965), 250–264. MR 178023, DOI https://doi.org/10.1007/BF01111683
- Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206 J. Hutchinson, Essential subdirect sums of rings (to appear).
S. U. Chase and C. Faith, Quotient rings and direct products of full linear rings, Math. Z. 88 (1965), 250-264. MR 31 #2281.
C. Faith, Lectures on injective modules and quotient rings, Lecture Notes in Math., no. 49, Springer-Verlag, New York, 1967. MR 37 #2791.
J. Hutchinson, Essential subdirect sums of rings (to appear).
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Keywords: Maximal quotient ring, complete quotient ring, classical quotient ring, full linear ring, essential extension, subdirect sums
Article copyright: © Copyright 1971 American Mathematical Society