Amalgamation extension in commutative ring theory: a survey
Abdelhaq El Khalfi, Hwankoo Kim & Najib Mahdou
Department oLaboratory of Topology, Algebra, Geometry and Discrete Mathematics, Faculty of
Sciences Ain Chock, Hassan II University of Casablanca, Morocco;
Hoseo University, Asan 31499, Republic of Korea;
Laboratory of Modelling and Mathematical Structures. Department of Mathematics, Faculty of
Science and Technology of Fez, Box 2202, University S. M. Ben Abdellah Fez, Morocco.
Pages 139-182 | Received 30 November 2021, Accepted 07 February 2022, Published 01 June 2022
Abstract
Let A and B be two rings, let J be an ideal of B and let f : A \longrightarrow B be a ring homomorphism. In this setting, we can consider the following subring of A \times B:
A \bowtie^{f} J = \{(a, f(a) + j)\mid a \in A, j \in J\}
called the amalgamation of A with B along J with respect to f (introduced and studied by D’Anna, Finocchiaro, and Fontana). This construction is a generalization of the amalgamated duplication of a ring along an ideal (introduced and studied by D’Anna and Fontana and denoted by A\bowtie I). In this paper, we survey known results concerning A \bowtie^{f} J.
Keywords: amalgamated duplication, amalgamation of ring, pullback, trivial ring extension.
MSC numbers: Primary 16B50; Secondary 13B99, 18A05.
Downloads: Full-text PDF