On the Vasconcelos inequality for the fiber multiplicity of modules. Issue 8 (3rd August 2018)

• Record Type: Journal Article
• Authors: Balakrishnan, R.; Jayanthan, A. V.
• Is Part Of: Communications in algebra. Volume 46:Issue 8(2018)
• Page Start: 3322
• Page End: 3333
• Publication Date: 2018-08-03
• Subjects: Buchsbaum-Rim function -- Buchsbaum-Rim polynomial -- fiber cone of modules -- Rees algebra of modules -- Vasconcelos inequality; 13D40 -- 13A30; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2017.1412452
• Languages: English
• ISSNs: 0092-7872

Abstract

ABSTRACT: Let ( R, 𝔪 ) be a Noetherian local ring of dimension d >0 with infinite residue field. Let M be a finitely generated proper R -submodule of a free R -module F with ℓ ( F ∕ M )<∞ and having rank r . In this article, we study the fiber multiplicity f 0 ( M ) of the module M . We prove that if ( R, 𝔪 ) is a two-dimensional Cohen–Macaulay local ring, thenf 0 ( M ) ≤ b r 1 ( M ) − b r 0 ( M ) + ℓ ( F ∕ M ) + μ ( M ) − r, where b r i ( M ) denotes the i th Buchsbaum-Rim coefficient of M .