AN AMALGAMATED DUPLICATION OF A RING ALONG AN IDEAL: THE BASIC PROPERTIES

DOI10.1142/S0219498807002326zbMATH Open1126.13002arXivmath/0605602OpenAlexW2153271808MaRDI QIDQ3595328

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Publication date: 10 August 2007

Published in: (Search for Journal in Brave)

Abstract: We introduce a new general construction, denoted by $RJoinE$, 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 $E^2=0$, $RJoinE$ coincides with the Nagata's idealization $RltimesE$.) After discussing the main properties of the amalgamated duplication $RJoinE$ in relation with pullback--type constructions, we restrict our investigation to the study of $RJoinE$ when $E$ is an ideal of $R$. Special attention is devoted to the ideal-theoretic properties of $RJoinE$ and to the topological structure of its prime spectrum.

Full work available at URL: https://arxiv.org/abs/math/0605602

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