Prüfer Conditions in an Amalgamated Duplication of a Ring Along an Ideal

Abstract

Abstract This paper investigates ideal-theoretic as well as homological extensions of the Prüfer domain concept to commutative rings with zero divisors in an amalgamated duplication of a ring along an ideal. The new results both compare and contrast with recent results on trivial ring extensions (and pullbacks) as well as yield original families of examples issued from amalgamated duplications subject to various Prüfer conditions. Key Words: Amalgamated duplication of a ring along an idealArithmetical ringFqp-ringGaussian ringPrüfer domainPrüfer ringSemihereditary ringWeak global dimension2010 Mathematics Subject Classification: 13F0513C1013C1113F3013D0516D4016E1016E60 Notes Communicated by F. Tartarone. To Marco Fontana for his 65th birthday.