Open Access(Jordan) derivation on amalgamated duplication of a ring along an ideal
Author(s) -
Khalid Louartiti,
Abdellah Mamouni,
Mohammed Tamekkante
Publication year - 2022
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.42803
Subject(s) - subring , semiprime , noncommutative geometry , mathematics , ideal (ethics) , semiprime ring , prime (order theory) , ring (chemistry) , minimal ideal , pure mathematics , noncommutative ring , discrete mathematics , combinatorics , maximal ideal , philosophy , chemistry , organic chemistry , epistemology
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 dened 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.