Geodesic
Monomial Modules and Graded Betti Numbers
Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 721-736.

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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. 
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M. Crupi; G. Restuccia. Monomial Modules and Graded Betti Numbers. Matematičeskie zametki, Tome 85 (2009) no. 5, pp. 721-736. http://geodesic.mathdoc.fr/item/MZM_2009_85_5_a7/

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