On a certain functional identity involving inverses in division rings and local rings
Makaleler > Tam Makale · 2024
Yazarlar: Nefise Cezayirlioglu, Çağrı DEMİR
JOURNAL OF ALGEBRA AND ITS APPLICATIONS, SCI İndekslerine Giren Dergi, Uluslararası, Wos, 2024, cilt -, ss ---
DOI: 10.1142/S0219498825502202
Özet
Let D be a division ring, sigma an automorphism of D and u is an element of D a fixed element. We determine the forms of additive maps f,g : D -> D satisfying the identity f(x)x(-1) + sigma(x)g(x(-1)) = u, for every nonzero x is an element of D. We show that f and g are both generalized sigma-derivations of D except possibly when sigma is the identity automorphism and D is an imperfect field of characteristic 2. We further study the same rational identity in the context of local rings under some mild assumptions.