Amalgamated algebras along an ideal

zbMATH Open1177.13043arXiv0901.1742MaRDI QIDQ3653959

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Publication date: 4 January 2010

Abstract: Let $f:AoB$ 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.

Full work available at URL: https://arxiv.org/abs/0901.1742

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