Amalgamated algebras along an ideal
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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.
Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, 2008, W. de Gruyter (accepted for publication)
Proceedings of the Fifth International Fez Conference on Commutative Algebra and Applications, 2008, W. de Gruyter (accepted for publication)