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Weakly Finite Conductor Property in Amalgamated Algebra

  • Haitham El AlaouiEmail author
Conference paper
Part of the Springer Proceedings in Mathematics & Statistics book series (PROMS, volume 228)

Abstract

Let \(f: A{\longrightarrow } B\) be a ring homomorphism and J be an ideal of B. In this paper, we investigate the transfer of weakly finite conductor property in amalgamation of A with B along J with respect to f (denoted by \(A{\bowtie }^{f}J\)), introduced and studied by D’Anna, Finocchiaro and Fontana in 2009 (see D’Anna et al. (Commutative Algebra and Applications. Walter De Gruyter Publisher, Berlin, pp. 55–172, 2009), D’Anna et al. (J Pure Appl Algebra 214:1633–1641, 2010)). Our results generate original examples which enrich the current literature with new families of examples of nonfinite conductor weakly finite conductor rings.

Keywords

Weakly finite conductor Finite conductor ring Coherent ring Amalgamated duplication Amalgamated algebra 

Notes

Acknowledgements

I would like to thank the referee for the useful suggestions and comments, which have greatly improved this article.

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Copyright information

© Springer International Publishing AG 2018

Authors and Affiliations

  1. 1.Laboratory of Geometric and Arithmetic Algebra, Faculty of Sciences Dhar Al MahrazSidi Mohamed Ben Abdellah UniversityFezMorocco

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