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 
to be an FL (full linear) ring if 
is isomorphic to the full ring of linear transformations of a left vector space over a division ring. 
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.
- [1] Stephen U. Chase and Carl Faith, Quotient rings and direct products of full linear rings, Math. Z. 88 (1965), 250–264. MR 0178023, https://doi.org/10.1007/BF01111683
- [2] Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206
- [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
