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Distributing tensor
product over direct product
Kenneth R. Goodearl |
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Vol. 43 (1972), No. 1, 107–110
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Abstract |
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This paper is an investigation of conditions on a module A under which the natural map  is an injection. The investigation leads to a theorem that a commutative von Neumann regular ring is self-injective if and only if the natural map  is an injection for all collections {Fα} and {Gβ} of free modules. An example is constructed of a commutative ring R for which the natural map ![R[[s]]⊗R [[t]] → R[[s,t]]](a112x.png) is not an injection. |
Mathematical Subject Classification
Primary: 16A50
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Milestones
Received: 28 July 1971
Published: 1 October 1972
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Authors |
| Kenneth R. Goodearl | |
| University of California, Santa
Barbara Santa Barbara CA United States |
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