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

    https://doi.org/10.1142/S0219498807002326Cited by:180 (Source: Crossref)

    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 E2 = 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.

    Dedicated to Luigi Salce, on his 60th birthday

    AMSC: 13A15, 13B99, 14A05