A formula for the associated Buchsbaum–Rim multiplicities of a direct sum of cyclic modules II. Issue 8 (3rd August 2019)

• Record Type: Journal Article
• Authors: Hayasaka, Futoshi
• Is Part Of: Communications in algebra. Volume 47:Issue 8(2019)
• Page Start: 3250
• Page End: 3263
• Publication Date: 2019-08-03
• Subjects: Buchsbaum–Rim function -- Buchsbaum–Rim multiplicity -- cyclic modules -- Hilbert–Samuel multiplicity; Primary 13H15 -- Secondary 13P99; Algebra -- Periodicals; 512.005
• DOI: 10.1080/00927872.2018.1555836
• Languages: English
• ISSNs: 0092-7872

Abstract

Abstract: The associated Buchsbaum–Rim multiplicities of a module are a descending sequence of non-negative integers. These invariants of a module are a generalization of the classical Hilbert–Samuel multiplicity of an ideal. In this article, we compute the associated Buchsbaum–Rim multiplicity of a direct sum of cyclic modules and give a formula for the second to last positive associated Buchsbaum–Rim multiplicity in terms of the ordinary Buchsbaum–Rim and Hilbert–Samuel multiplicities. This is a natural generalization of a formula given by Kirby and Rees.