Regular modules
HTML articles powered by AMS MathViewer
- by David J. Fieldhouse PDF
- Proc. Amer. Math. Soc. 32 (1972), 49-51 Request permission
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
- P. M. Cohn, On the free product of associative rings, Math. Z. 71 (1959), 380–398. MR 106918, DOI 10.1007/BF01181410
- D. J. Fieldhouse, Pure theories, Math. Ann. 184 (1969), 1–18. MR 252479, DOI 10.1007/BF01350610
- R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056
Additional Information
- © Copyright 1972 American Mathematical Society
- 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