Freeness of orthogonal modules |
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Authors: | Jacques Allard Kee Yuen Lam |
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Institution: | Université de Moncton, Moncton, N.B., Canada E1A 3E9;University of British Columbia, Vancouver, B.C., Canada V6T 1W5 |
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Abstract: | A finitely generated module M over a commutative ring with unit R is said to be orthogonal stably free of type (n, m) if M is isomorphic to the solution space of a mxn matrix α such that ααt=Im. Geramita and Pullman have defined “generic” orthogonal stably free modules for each possible type and have obtained results on the freeness of these modules and on the supremum of the ranks of their free direct summands. We obtain further results of this type, concerning the generic modules of Geramita and Pullman as well as their sums with free modules and, in a few cases, their iterated sums. The last results are related to a theorem of T.Y. Lam stating that the iterated sum r · M of a stably free module M is free if r is greater than some lower bound. This lower bound is shown to be best possible in some cases. |
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