A generalization of an inequality of Lech relating multiplicity and colength*. Issue 6 (3rd June 2019)

• Record Type: Journal Article
• Authors: Huneke, Craig; Smirnov, Ilya; Validashti, Javid
• Is Part Of: Communications in algebra. Volume 47:Issue 6(2019)
• Page Start: 2436
• Page End: 2449
• Publication Date: 2019-06-03
• Subjects: Lech's inequality -- multiplicity; 13H15 -- 13D40; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1482307
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: We study conjectured generalizations of a formula of Lech which relates the multiplicity of a finite colength ideal in an equicharacteristic local ring to its colength and prove one of these generalizations involving the multiplicity of the maximal ideal times the finite colength ideal. We also propose a Lech-type formula that relates multiplicity and the number of generators. We prove the conjecture in dimension three and establish a weaker result in full generality.