# Trivial Extensions of Local Rings and a Conjecture of Costa

@article{Kabbaj2002TrivialEO, title={Trivial Extensions of Local Rings and a Conjecture of Costa}, author={S. Kabbaj and Najib Mahdou}, journal={arXiv: Commutative Algebra}, year={2002} }

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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