(Jordan) derivation on amalgamated duplication of a ring along an ideal

  • Khalid Louartiti Hassan II University
  • Abdellah Mamouni Moulay Ismail University
  • Mohammed Tamekkante Moulay Ismail University

Resumo

Let A be a ring and I be an ideal of A. The amalgamated duplication of A along I is the subring of A × A defined by $A\bowtie I := {(a, a + i) |a ∈ A, i ∈ I}$.  In this paper, we characterize $A\bowtie I$  over which any (resp. minimal)  prime  ideal  is  invariant  under  any  derivation  provided  that  A  is semiprime.  When A is noncommutative prime, then $A\bowtie I$  is noncommutative semiprime (but not prime except if I = (0)).  In this case, we prove that any map of $A\bowtie I$   which is both Jordan and Jordan triple derivation is a derivation.

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Publicado
2021-12-16
Seção
Artigos