Modules with Finite F -representation Type
نویسنده
چکیده
Finitely generated modules with finite F -representation type (or FFRT for short) over Noetherian (local) rings of prime characteristic p are studied. If a ring R has FFRT or, more generally, if a faithful R-module has FFRT, then tight closure commutes with localizations over R. We also define F -contributors and use them to give an effective way to characterize tight closure. Then we show lime→∞ #( M,Mi) (apd)e always exists under that assumption that (R, m) satisfies the Krull-Schmidt condition and M has FFRT by {M1, M2, . . . , Ms}, in which all the Mi’s are indecomposable R-modules belonging to distinct isomorphism classes and a = [R/m : (R/m)p].
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