A subdirect decomposition of semiprime rings and its application to maximal quotient rings
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- by Louis Halle Rowen PDF
- Proc. Amer. Math. Soc. 46 (1974), 176-180 Request permission
Abstract:
Levy [2] has examined semiprime rings which are irredundant subdirect products of prime rings. In this note we look at the role of inessential prime ideals and see how every semiprime ring is a subdirect product of (i) a semiprime ring which is an irredundant subdirect product of prime rings, and (ii) a semiprime (nonprime) ring, all of whose prime ideals are essential. This leads to a direct sum decomposition of maximal left quotient rings of semiprime rings with left singular ideal zero.References
- Carl Faith, Lectures on injective modules and quotient rings, Lecture Notes in Mathematics, No. 49, Springer-Verlag, Berlin-New York, 1967. MR 0227206
- Lawrence Levy, Unique subdirect sums of prime rings, Trans. Amer. Math. Soc. 106 (1963), 64–76. MR 142567, DOI 10.1090/S0002-9947-1963-0142567-9
- Louis Halle Rowen, Maximal quotients of semiprime PI-algebras, Trans. Amer. Math. Soc. 196 (1974), 127–135. MR 347887, DOI 10.1090/S0002-9947-1974-0347887-8
Additional Information
- © Copyright 1974 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 46 (1974), 176-180
- MSC: Primary 16A12
- DOI: https://doi.org/10.1090/S0002-9939-1974-0349728-7
- MathSciNet review: 0349728