Let $f : A \rightarrow B$ be a ring homomorphism and J an ideal of B. In this paper, we initiate a systematic study of a new ring construction called the “amalgamation of A with B along J with respect to f ”. This construction finds its roots in a paper by J.L. Dorroh appeared in 1932 and provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D’Anna and Fontana in 2007, and other classical constructions such as the A + XB[X] and A + XB[[X]] constructions, the CPI-extensions of Boisen and Sheldon, the D + M constructions and the Nagata’s idealization.

### Amalgamated algebras along an ideal

#### Abstract

Let $f : A \rightarrow B$ be a ring homomorphism and J an ideal of B. In this paper, we initiate a systematic study of a new ring construction called the “amalgamation of A with B along J with respect to f ”. This construction finds its roots in a paper by J.L. Dorroh appeared in 1932 and provides a general frame for studying the amalgamated duplication of a ring along an ideal, introduced and studied by D’Anna and Fontana in 2007, and other classical constructions such as the A + XB[X] and A + XB[[X]] constructions, the CPI-extensions of Boisen and Sheldon, the D + M constructions and the Nagata’s idealization.
##### Scheda breve Scheda completa Scheda completa (DC)
978-3-11-020746-0
Nagata’s idealization; Pullback; Amalgamated duplication
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Utilizza questo identificativo per citare o creare un link a questo documento: http://hdl.handle.net/20.500.11769/89591
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