Prüfer property in amalgamated algebras along an ideal

Abstract

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.

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Correspondence to Moutu Abdou Salam Moutui.

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Mahdou, N., Moutui, M.A.S. Prüfer property in amalgamated algebras along an ideal. Ricerche mat 69, 111–120 (2020). https://doi.org/10.1007/s11587-019-00451-1

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Keywords

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

Mathematics Subject Classification

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