Trivial Extensions of Local Rings and a Conjecture of Costa

Details Trivial Extensions of Local Rings and a Conjecture of Costa Trivial Extensions of Local Rings and a Conjecture of Costa

2006-06-27

arxiv.org/abs/math/0606694v1

Lecture Notes in Pure and Applied in Mathematics - Dekker 231 (2002) 301-311

Mathematics

Commutative Algebra

11 pages

Scientific paper

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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