A Note on C-graded Modules over an Affine Semigroup Ring K[c]
نویسنده
چکیده
Let C ⊂ Z be an affine semigroup, R = K[C] its semigroup ring, and *modC R the category of finitely generated “C-graded” R-modules (i.e., Z -graded modules M with M = ⊕ c∈C Mc). When R is Cohen-Macaulay and simplicial, we show that information on M ∈ *modC R such as depth, CohenMacaulayness, and (Sn) condition, can be read off from numerical invariants of the minimal irreducible resolution (i.e., minimal injective resolution in the category *modC R) of M . Other topics of C-graded modules are also discussed.
منابع مشابه
Notes on C-graded Modules over an Affine Semigroup Ring K[c]
Let C ⊂ N be an affine semigroup, and R = K[C] its semigroup ring. This paper is a collection of various results on “C-graded” R-modules M = ⊕ c∈C Mc, especially, monomial ideals of R. For example, we show the following: If R is normal and I ⊂ R is a radicalmonomial ideal (i.e., R/I is a generalization of Stanley-Reisner rings), then the sequentially Cohen-Macaulay property of R/I is a topologi...
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