A note on modules over a commutative regular ring
HTML articles powered by AMS MathViewer
- by Mark L. Teply PDF
- Proc. Amer. Math. Soc. 29 (1971), 267-268 Request permission
Abstract:
An example is given of a commutative, von Neumann regular ring R, which has a module A satisfying the following conditions: (1) $T(A) = \{ a \in A|(0:a)$ is an essential ideal of R} is a cyclic R-module; (2) $A/T(A)$ is a cyclic R-module; and (3) $T(A)$ is not a direct summand of A. This answers in the negative a question raised by R. S. Pierce.References
- J. S. Alin and S. E. Dickson, Goldie’s torsion theory and its derived functor, Pacific J. Math. 24 (1968), 195–203. MR 227249
- 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 1971 American Mathematical Society
- Journal: Proc. Amer. Math. Soc. 29 (1971), 267-268
- MSC: Primary 13.40
- DOI: https://doi.org/10.1090/S0002-9939-1971-0276214-2
- MathSciNet review: 0276214