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

By Marco D'anna, Marco Fontana. 2006

278 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/3144939b2bca5ae8cd1066cddc17ceb9f1b0bcb8

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In Algebra and Number Theory

In Geometry and Topology

Citations in the corpus

Properties of chains of prime ideals in an amalgamated algebra along an ideal (2010, background): “This construction is a generalization of the amalgamated duplication of a ring along an ideal (introduced and studied in [9], [6], [10] and in [20]).”
Amalgamated algebras along an ideal (2009, background): “A particular case of the construction introduced above is the amalgamated d uplication of a ring [6].”
New Algebraic Properties of an Amalgamated Algebra Along an Ideal (2016, background): “A particular case of this type of pullback is the amalgamated duplication A I , where A is a local ring and I an ideal of A (see [12] and [13]).”
Von Neumann Regular and Related Elements in Commutative Rings (2012, background): “As in [12], the amalgamated duplication of the ring R along the ideal I is defined to be the subring R .”