Jordan homoderivation behavior of generalized derivations in prime rings

Nripendu Bera; Basudeb Dhara

doi:10.3842/umzh.v75i9.7241

Nripendu Bera Department of Mathematics, Jadavpur University, Kolkata, India
Basudeb Dhara Department of Mathematics, Belda College, Belda, Paschim Medinipur, India

DOI: https://doi.org/10.3842/umzh.v75i9.7241

Анотація

УДК 512.5

Поведінка жорданової гомопохідної для узагальнених похідних на простих кільцях

Припустимо, що $R$ – просте кільце з ${\rm char}(R)\neq 2$, а $f(\xi_1,\ldots,\xi_n)$ – нецентральний мультилінійний поліном над $C( = Z(U)),$ де $U$ --- фактор-кільце Утумі $R.$ Адитивне відображення $h\colon R\rightarrow R$ називається гомопохідною, якщо $h(ab) = h(a)h(b)+h(a)b +ah(b)$ для всіх $a,b\in R.$ Досліджено поведінку трьох узагальнених похідних $F,$ $G$ та $H$ на $R$, що задовольняють умову $$F(\xi^2) = G(\xi)^2+H(\xi)\xi+\xi H(\xi)$$ для всіх $\xi \in f(R) = \{f(\xi_1,\ldots,\xi_n) | \xi_1,\ldots,\xi_n\in R\}.$

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