Generalized skew derivations implemented by elementary operators
Eremita, Daniel ; Gogić, Ilja, 1982- ; Ilišević, Dijana
Naj bo ▫$R$▫ polprakolobar z maksimalnim desnim kolobarjem kvocientov ▫$Q_{mr}$▫. Aditivni preslikavi ▫$d: R \to Q_{mr}$▫ pravimo posplošeno poševno odvajanje, če obstaja tak endomorfizem ▫$\sigma$▫ ...kolobarja ▫$R$▫ in taka preslikava ▫$\delta: R \to Q_{mr}$▫, da je ▫$d(xy) = \delta(x)y + \sigma(x)d(y)$▫ za vse▫ $x,y \in R▫$. Ob predpostavki, da je endomorfizem ▫$\sigma$▫ surjektiven, opišemo strukturo poljubnega posplošenega poševnega odvajanja, za katerega obstajajo taki elementi ▫$a_i, b_i \in Q_{mr}$▫, da je ▫$d(x) = a_1 xb_1 + \dots + a_nxb_n$▫ za vse ▫$x \in R$▫.
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