We introduce a new general construction, denoted by $R \bowtie E$, 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 $E^2 = 0$, $R \bowtie E$ coincides with the Nagata's idealization $RE$.) After discussing the main properties of the amalgamated duplication $R \bowtie E$ in relation with pullback-type constructions, we restrict our investigation to the study of $R \bowtie E$ when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of $R \bowtie E$ and to the topological structure of its prime spectrum.

An amalgamated duplication of a ring along an ideal: the basic properties

D'ANNA, Marco;
2007

Abstract

We introduce a new general construction, denoted by $R \bowtie E$, 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 $E^2 = 0$, $R \bowtie E$ coincides with the Nagata's idealization $RE$.) After discussing the main properties of the amalgamated duplication $R \bowtie E$ in relation with pullback-type constructions, we restrict our investigation to the study of $R \bowtie E$ when E is an ideal of R. Special attention is devoted to the ideal-theoretic properties of $R \bowtie E$ and to the topological structure of its prime spectrum.
Idealization; Pullback; Zariski topology
File in questo prodotto:
Non ci sono file associati a questo prodotto.

I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.

Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/35755
Citazioni
  • ???jsp.display-item.citation.pmc??? ND
  • Scopus ND
  • ???jsp.display-item.citation.isi??? 135
social impact