On the Asymptotic Values of Length Functions in Krull and Finitely Generated Commutative Monoids
نویسنده
چکیده
Let M be a commutative cancellative atomic monoid. We consider the behavior of the asymptotic length functions ̄̀(x) and L̄(x) on M . If M is finitely generated and reduced, then we present an algorithm for the computation of both ̄̀(x) and L̄(x) where x is a nonidentity element of M . We also explore the values that the functions ̄̀(x) and L̄(x) can attain when M is a Krull monoid with torsion divisor class group, and extend a well-known result of Zaks and Skula by showing how these values can be used to characterize when M is half-factorial.
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تاریخ انتشار 2002