An amalgamated duplication of a ring along an ideal: the basic properties
arXiv:math/0605602
Abstract
We introduce a new general construction, denoted by $R\JoinE$, called the amalgamated duplication of a ring along an --module , that we assume to be an ideal in some overring of . (Note that, when , $R\JoinE$ coincides with the Nagata's idealization .) After discussing the main properties of the amalgamated duplication $R\JoinE$ in relation with pullback--type constructions, we restrict our investigation to the study of $R\JoinE$ when is an ideal of . Special attention is devoted to the ideal-theoretic properties of $R\JoinE$ and to the topological structure of its prime spectrum.
Replace a previous version. Journal of Algebra and Applications (to appear)