Amalgamated algebras along an ideal

2009/01/13 by D'Anna, Marco, Finocchiaro, Carmelo Antonio, Fontana, Marco · 3 citations
#13B99 #13E05 #13F20 #14A05 #Algebraic Geometry (math.AG) #Commutative Algebra (math.AC) #FOS: Mathematics

paper · doi:10.48550/arxiv.0901.1742

Abstract

Let f:A → 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.

Cited by

• On 2-absorbing submodules and their Amalgamations
• Almost Noetherian rings and modules
• Some Extensions of Endo-Noetherian Rings

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