We introduce a new general construction, denoted by $R \bowtie E$, called the amalgamated duplication of a ring R along an R-module E, that we assume to be an ideal in some overring of R. (Note that, when $E^2 = 0$, $R \bowtie E$ coincides with the Nagata's idealization $RE$.) After discussing the main properties of the amalgamated duplication $R \bowtie E$ in relation with pullback-type constructions, we restrict our investigation to the study of $R \bowtie E$ when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of $R \bowtie E$ and to the topological structure of its prime spectrum.
An amalgamated duplication of a ring along an ideal: the basic properties
D'ANNA, Marco;
2007-01-01
Abstract
We introduce a new general construction, denoted by $R \bowtie E$, called the amalgamated duplication of a ring R along an R-module E, that we assume to be an ideal in some overring of R. (Note that, when $E^2 = 0$, $R \bowtie E$ coincides with the Nagata's idealization $RE$.) After discussing the main properties of the amalgamated duplication $R \bowtie E$ in relation with pullback-type constructions, we restrict our investigation to the study of $R \bowtie E$ when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of $R \bowtie E$ and to the topological structure of its prime spectrum.File in questo prodotto:
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