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On the arithmetic of stable domains
Aqsa Bashir1, Alfred Geroldinger1, Andreas Reinhart1
1Institut für Mathematik und Wissenschaftliches Rechnen, Karl-Franzens-Universität Graz, NAWI Graz, Graz, Austria.
Abstract:
A commutative ring R is stable if every non-zero ideal I of R is projective over its ring of endomorphisms. Motivated by a paper of Bass in the 1960s, stable rings have received wide attention in the literature ever since then. Much is known on the algebraic structure of stable rings and on the relationship of stability with other algebraic properties such as divisoriality and the 2-generator property. In the present paper, we study the arithmetic of stable integral domains, with a focus on arithmetic properties of semigroups of ideals of stable orders in Dedekind domains.
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