Amalgamated algebras along an ideal

Details Amalgamated algebras along an ideal Amalgamated algebras along an ideal

2009-01-13

arxiv.org/abs/0901.1742v1

Mathematics

Commutative Algebra

Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, 2008, W. de Gruyter (accepted f

Scientific paper

Let $f:A \to B$ 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.

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