An amalgamated duplication of a ring along an ideal: the basic properties
Abstract
We introduce a new general construction, denoted by R, 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 E2 =0, R coincides with the Nagata's idealization R E.) After discussing the main properties of the amalgamated duplication R in relation with pullback--type constructions, we restrict our investigation to the study of R when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of R and to the topological structure of its prime spectrum.
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