Let {R n , m n } n≥0 be an infinite sequence of regular local rings with R n+1 birationally dominating R n and m n R n+1 a principal ideal of R n+1 for each n. We examine properties of the integrally closed local domain S = n≥0 R n .
In this paper we study the Weak Lefschetz property of two classes of standard graded Artinian Gorenstein algebras associated in a natural way to the Apéry set of numerical semigroups. To this aim we also prove a general result about the transfer of the Weak Lefschetz property from an Artinian Gorenstein algebra to its quotients modulo a colon ideal. MSC: 13A30; 13E10; 13H10.
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