A note on modules over a commutative regular ring
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.
-  J. S. Alin and S. E. Dickson, Goldie’s torsion theory and its derived functor, Pacific J. Math. 24 (1968), 195–203. MR 0227249
-  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
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Keywords: Regular ring, torsion submodule, Boolean ring, direct summand, cyclic module
Article copyright: © Copyright 1971 American Mathematical Society