Projective Modules and Complete Intersections |
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Authors: | Raja Sridharan |
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Institution: | (1) School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay, 400 005, India. e-mail |
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Abstract: | Let A be a Noetherian ring of dimension n and P be a projective A module of rank n having trivial determinant. It is proved that if n is even and the image of a generic element g P* is a complete intersection, then P] = Q A] in K0(A) for some projective A module Q of rank n – 1. Further, it is proved that if n is odd, A is Cohen–Macaulay and P] = Q A] in K0(A) for some projective A module Q of rank n – 1, then P has a unimodular element. |
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Keywords: | projective module unimodular element complete intersection |
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