On a certain functional identity involving inverses in division rings and local rings
Makaleler > Tam Makale · 2024
Yazarlar: Nefise Cezayirlioğlu, Çağrı Demir
Journal of Algebra and Its Applications, Uluslararası, Wos, 2024, cilt 24
DOI: 10.1142/s0219498825502202
Özet
Let [Formula: see text] be a division ring, [Formula: see text] an automorphism of [Formula: see text] and [Formula: see text] a fixed element. We determine the forms of additive maps [Formula: see text] satisfying the identity [Formula: see text] for every nonzero [Formula: see text]. We show that [Formula: see text] and [Formula: see text] are both generalized [Formula: see text]-derivations of [Formula: see text] except possibly when [Formula: see text] is the identity automorphism and [Formula: see text] is an imperfect field of characteristic [Formula: see text]. We further study the same rational identity in the context of local rings under some mild assumptions.