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We introduce a new general construction, denoted by R ⋈ 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 ⋈ E coincides with the Nagata's idealization R ⋉ E.). After discussing the main properties of the amalgamated duplication R ⋈ E in relation with pullback-type constructions, we restrict our investigation to the study of R ⋈ E when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of R ⋈ E and to the topological structure of its prime spectrum.
D’Anna et al. (Fri,) studied this question.