LIE MAPS ON ALTERNATIVE RINGS PRESERVING IDEMPOTENTS

Author(s)

Ferreira, Bruno Leonardo Macedo ^[1] ; Guzzo, Jr., Henrique ^[2] ; Kaygorodov, Ivan ^{[3, 4]}

Affiliation

^[1] Fed Univ Technol, Professora Laura Pacheco Bastos Ave, 800, BR-85053510 Guarapuava - Brazil

^[2] Univ Sao Paulo, Inst Math, Matao St, 1010, BR-05508090 Sao Paulo - Brazil

^[3] Fed Univ ABC, Estados Ave, 5001, BR-09210580 Santo Andre, SP - Brazil

^[4] Moscow Ctr Fundamental & Appl Math, Moscow 119991 - Russia

• Document type: Journal article
• Source: Colloquium Mathematicum; v. 166, n. 2 APR 2021.
• Web of Science Citations: 0

Abstract

Let R and R' be unital 2,3-torsion free alternative rings and phi : R -> R' be a surjective Lie multiplicative map that preserves idempotents. Assume that R has a nontrivial idempotent. Under certain assumptions on R, we prove that phi is of the form psi + tau, where zb is either an isomorphism or the negative of an anti-isomorphism of R onto R' and tau is an additive mapping of R into the centre of R' which maps commutators to zero. (AU)

• FAPESP's process: 19/03655-4 - Graded structures
• Grantee: Ivan Kaygorodov
• Support Opportunities: Scholarships abroad - Research