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Todd Trimble
Todd Trimble
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As @Jeremy Rickard has mentioned, the impossibility of the problem haswas shown by Osofsky in 1968. But it is interesting that there is another article dateddating back to 1968 (again  !) that proves the same thing. See Cateforis, Sandomerski, The singular submodule spiltssplits off, J. Algebra, 10  (1968), 149-165, Theorem 4.1. This article haswas received by J. Algebra aton November 20, 1967 while Osofsky's paper haswas received by Proc. Amer. Math. Soc. aton July 10, 1967. I hope this information meets the expectations.

As @Jeremy Rickard has mentioned the impossibility of the problem has shown by Osofsky in 1968. But it is interesting that there is another article dated back to 1968 (again  !) that proves the same thing. See Cateforis, Sandomerski, The singular submodule spilts off, J. Algebra, 10(1968), 149-165, Theorem 4.1. This article has received by J. Algebra at November 20, 1967 while Osofsky's paper has received by Proc. Amer. Math. Soc. at July 10, 1967. I hope this information meets the expectations.

As @Jeremy Rickard has mentioned, the impossibility was shown by Osofsky in 1968. But it is interesting that there is another article dating back to 1968 (again!) that proves the same thing. See Cateforis, Sandomerski, The singular submodule splits off, J. Algebra, 10  (1968), 149-165, Theorem 4.1. This article was received by J. Algebra on November 20, 1967 while Osofsky's paper was received by Proc. Amer. Math. Soc. on July 10, 1967. I hope this information meets the expectations.

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user38133
user38133

As @Jeremy Rickard has mentioned the impossibility of the problem has shown by Osofsky in 1968. But it is interesting that there is another article dated back to 1968 (again !) that proves the same thing. See Cateforis, Sandomerski, The singular submodule spilts off, J. Algebra, 10(1968), 149-165, Theorem 4.1. This article has received by J. Algebra at November 20, 1967 while Osofsky's paper has received by Proc. Amer. Math. Soc. at July 10, 1967. I hope this information meets the expectations.