Quotient full linear rings
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.
-  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
-  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. MR 0178023 (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. MR 0227206 (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