• Corpus ID: 14597668

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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