Quotient full linear rings
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- by John J. Hutchinson
- Proc. Amer. Math. Soc. 28 (1971), 375-378
- DOI: https://doi.org/10.1090/S0002-9939-1971-0424867-8
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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
- Stephen U. Chase and Carl Faith, Quotient rings and direct products of full linear rings, Math. Z. 88 (1965), 250–264. MR 178023, DOI 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).
Bibliographic Information
- © Copyright 1971 American Mathematical Society
- 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