Prüfer property in amalgamated algebras along an ideal

  • Najib Mahdou
  • Moutu Abdou Salam MoutuiEmail author


Let \(f : A \rightarrow B\) be a ring homomorphism and J be an ideal of B. In this paper, we give a characterization of zero divisors of the amalgamation which is a generalization of Maimani’s and Yassemi’s work (see Maimani and Yassemi in J Pure Appl Algebra 212(1):168–174, 2008). Furthermore, we investigate the transfer of Prüfer domain concept to commutative rings with zero divisors in the amalgamation of A with B along J with respect to f (denoted by \(A\bowtie ^fJ),\) introduced and studied by D’Anna et al. (Commutative algebra and its applications, Walter de Gruyter, Berlin, 2009, J Pure Appl Algebra 214:1633–1641, 2010). Our results recover well known results on duplications. The main applications constist in the construction of new original classes of Prüfer rings that are not Gaussian and Prüfer rings with weak global dimension strictly greater than 1.


Amalgamated algebra along an ideal Prüfer rings Gaussian rings Amalgamated duplication Trivial rings extension 

Mathematics Subject Classification

13F05 13A15 13E05 13F20 13F30 13D05 16D40 



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Copyright information

© Università degli Studi di Napoli "Federico II" 2019

Authors and Affiliations

  1. 1.Department of Mathematics, Faculty of Science and Technology of FezUniversity S. M. Ben AbdellahFezMorocco
  2. 2.Department of Mathematics, College of ScienceKing Faisal UniversityAl-AhsaaSaudi Arabia

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