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Trivial Extensions of Local Rings and a Conjecture of Costa

S. Kabbaj·N. Mahdou
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Abstract

This paper partly settles a conjecture of Costa on (n,d)-rings, i.e., rings in which n-presented modules have projective dimension at most d. For this purpose, a theorem studies the transfer of the (n,d)-property to trivial extensions of local rings by their residue fields. It concludes with a brief discussion -backed by original examples- of the scopes and limits of our results.

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S. Kabbaj, N. Mahdou. 2006-06-27. Trivial Extensions of Local Rings and a Conjecture of Costa. https://arxiv.org/abs/math/0606694

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