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About: Invertible module     Goto   Sponge   NotDistinct   Permalink

An Entity of Type : yago:Whole100003553, within Data Space : dbpedia.demo.openlinksw.com associated with source document(s)

Type: yago:WikicatMathematicalStructuresyago:Artifact100021939yago:Object100002684yago:PhysicalEntity100001930yago:YagoGeoEntityyago:YagoPermanentlyLocatedEntityyago:Structure104341686yago:Whole100003553 New Facet based on Instances of this Class

In mathematics, particularly commutative algebra, an invertible module is intuitively a module that has an inverse with respect to the tensor product. Invertible modules form the foundation for the definition of invertible sheaves in algebraic geometry. Formally, a finitely generated module M over a ring R is said to be invertible if it is locally a free module of rank 1. In other words, for all primes P of R. Now, if M is an invertible R-module, then its dual M* = Hom(M,R) is its inverse with respect to the tensor product, i.e. .