The amalgamated duplication of a ring along a multiplicative-canonical ideal

Abstract

After recalling briefly the main properties of the amalgamated duplication of a ring $R$ along an ideal $I$, denoted by $R\JoinI$, we restrict our attention to the study of the properties of $R\JoinI$, when $I$ is a multiplicative canonical ideal of $R$ \cite{hhp}. In particular, we study when every regular fractional ideal of $R\bowtie I$ is divisorial.

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• Prûfer property in amalgamated algebras along an ideal
• Self injective property in amalgamated algebra along an ideal
• Gaussian property in amalgamated algebras along an ideal
• Prufer conditions in an amalgamated duplication of a ring along an ideal
• On Armendariz-like properties in Amalgamated algebras along ideals
• Gorenstein global dimension of an amalgamated duplication of a coherent ring along an ideal
• When an amalgamated duplication of a ring along an ideal is quasi-Frobenius