Amalgamated algebras along an ideal

By Marco D'anna, C. Finocchiaro, Marco Fontana. 2009

156 citations recorded by the source corpus.

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.

Subfields: Algebra and Number Theory, Geometry and Topology

View Paper: https://www.semanticscholar.org/paper/59db6dca0a7cf4a05830ffc2e42e46cc283d3835

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In Algebra and Number Theory

1. C. Finocchiaro
2. Marco Fontana
3. Marco D'anna

In Geometry and Topology

1. Marco Fontana
2. C. Finocchiaro
3. Marco D'anna

Citations in the corpus

• New Algebraic Properties of an Amalgamated Algebra Along an Ideal (2016, methodology): “In particular, after recalling (in Section 2) some basic properties proved in [10], needed in the present article, we provide a complete description of the prime spectrum of A J (Corollary 2.”