This article is cited in 5 papers

Monomial Modules and Graded Betti Numbers

M. Crupi, G. Restuccia

University of Messina

Abstract: Let $K$ be a field, $S=K[x_1,\dots,x_n]$, the polynomial ring over $K$, and let $F$ be a finitely generated graded free $S$-module with homogeneous basis. Certain invariants, such as the Castelnuovo–Mumford regularity and the graded Betti numbers of submodules of $F$, are studied; in particular, the componentwise linear submodules of $F$ are characterized in terms of their graded Betti numbers.

Keywords: graded ring, graded module, minimal graded free resolution, graded Betti number, polynomial ring, Gröbner basis, syzygy module.

UDC: 512.626

Received: 18.01.2008

DOI: 10.4213/mzm6909

 English version: Mathematical Notes, 2009, 85:5, 690–702

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