A note on modules over a commutative regular ring
Mark L. Teply
Proc. Amer. Math. Soc. 29 (1971), 267-268
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Abstract: An example is given of a commutative, von Neumann regular ring R, which has a module A satisfying the following conditions: (1) is an essential ideal of R} is a cyclic R-module; (2) is a cyclic R-module; and (3) is not a direct summand of A. This answers in the negative a question raised by R. S. Pierce.
S. Alin and S.
E. Dickson, Goldie’s torsion theory and its derived
functor, Pacific J. Math. 24 (1968), 195–203.
0227249 (37 #2834)
S. Pierce, Modules over commutative regular rings, Memoirs of
the American Mathematical Society, No. 70, American Mathematical Society,
Providence, R.I., 1967. MR 0217056
- J. S. Alin and S. E. Dickson, Goldie's torsion theory and its derived functor, Pacific J. Math. 24 (1968), 195-203. MR 37 #2834. MR 0227249 (37:2834)
- 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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