Commutative Ring Theory

2 Maximality Properties in Numerical Semigroups, with Applications to One-Dimensional Analytically Irreducible Local Domains

Valentina Barucci*, *†

Dipartimento di Matematica Università di Roma “La Sapienza” 00185 Roma ITALY

David E. Dobbs*, **

Department of Mathematics University of Tennessee Knoxville, TN 37996-1300 U.S.A.

Marco Fontana*, †

Facoltà di Scienze Terza Universitá degli studi di Roma 00146 Roma ITALY

1. Introduction

Suppose that A is a Noetherian local (commutative integral) domain which is analytically irreducible and of Krull dimension at most 1; as we noted in [BDF2, Remark 5(b)], this is equivalent to supposing that A is a Noetherian conducive domain, in the sense of [BDF1]. Thus (apart from the trivial case of a field A