Fiting ideals Sample Clauses

Fiting ideals.ย โ€Œ In this subsection we recall the higher Fitting ideals of finitely generated modules over ๐‘…. To do this we assume that ๐‘€ is finitely generated and fix a presentation ๐‘…๐‘› ๐œ™ ๐‘…๐‘š โ†’ ๐‘€ โ†’ 0. We say that ๐‘€ has a quadratic presentation if one can take ๐‘› = ๐‘š in such a presโˆ’โ†’entation. For any integer ๐‘Ÿ โ‰ค ๐‘š the map ๐œ™ induces a pairing ๐‘… ๐‘… ๐‘… ฮฆ๐‘Ÿ : ๐‘šโˆ’๐‘Ÿ ๐‘…๐‘› โŠ— ๐‘šโˆ’๐‘Ÿ ๐‘…๐‘š,โˆ— โ†’ ๐‘…, ๐‘Ž โŠ— ๐‘ โ†ฆโ†’ ๐‘ (( ๐‘šโˆ’๐‘Ÿ ๐œ™)(๐‘Ž))
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