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Regular modules


Author: David J. Fieldhouse
Journal: Proc. Amer. Math. Soc. 32 (1972), 49-51
MSC: Primary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1972-0292882-4
MathSciNet review: 0292882
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Abstract: Pierce [3] has shown that over a commutative regular ring every finitely generated submodule of an n-generated module is n-generated, and then has asked if this result holds for noncommutative regular rings. Here the result is shown for regular modules over any associative ring, which answers Pierce's question since a ring is regular if and only if every module is regular.


References [Enhancements On Off] (What's this?)

  • [1] P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959), 380-398. MR 21 #5648. MR 0106918 (21:5648)
  • [2] D. J. Fieldhouse, Pure theories Math. Ann. 184 (1969), 1-18. MR 40 #5699. MR 0252479 (40:5699)
  • [3] R. S. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc. No. 70 (1967). MR 36 #151. MR 0217056 (36:151)

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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1972-0292882-4
Keywords: Regular module, regular ring, pure submodule, n-generated module
Article copyright: © Copyright 1972 American Mathematical Society

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