Notes on C-graded Modules over an Affine Semigroup Ring K[c]
نویسنده
چکیده
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 topological property of the “geometric realization” of the cell complex associated with I. Moreover, we can give a squarefree modules/constructible sheaves version of this result. We also show that if R is normal and I ⊂ R is a Cohen-Macaulay monomial ideal then √ I is Cohen-Macaulay again.
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A Note on C-graded Modules over an Affine Semigroup Ring K[c]
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