An amalgamated duplication of a ring along an ideal: the basic properties
نویسندگان
چکیده
We introduce a new general construction, denoted by R 1 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 = 0, R1E coincides with the Nagata’s idealization R⋉E.) After discussing the main properties of the amalgamated duplication R 1E in relation with pullback–type constructions, we restrict our investigation to the study of R1E when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of R1E and to the topological structure of its prime spectrum.
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