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On (anti-)multiplicative generalized derivationsEremita, Daniel ; Ilišević, DijanaNaj bo ▫$R$▫ polprakolobar in naj bosta ▫$F, f \colon R \to R$▫ taki (ne nujno aditivni) preslikavi, da je ▫$F(xy) = F(x)y + xf(y)$▫ za vse ▫$x,y \in R$▫. Denimo, da obstajata taki celi števili ▫$m$▫ ... in ▫$n$▫, da velja ▫$F(uv) = mF(u)F(v) + nF(v)F(u)$▫ za vse elemente ▫$u$▫, ▫$v$▫ neničelnega ideala ▫$I$▫ kolobarja ▫$R$▫. Ob določenih blagih predpostavkah za polprakolobar ▫$R$▫ dokažemo, da obstaja tak ▫$c \in C(I^{\bot\bot})$▫, da je ▫$c = (m+n)c^2$▫, ▫$nc[I^{\bot\bot}, I^{\bot\bot}] = 0$▫ in ▫$F(x) = cx$▫ za vse ▫$x \in I^{\bot\bot}$▫. Glavni rezultat je nato uporabljen v primeru, ko je preslikava ▫$F$▫ multiplikativna ali antimultiplikativna na idealu ▫$I$▫.Source: Glasnik matematički. Serija 3. - ISSN 0017-095X (Vol. 47, no. 1, 2012, str. 105-118)Type of material - article, component part ; adult, seriousPublish date - 2012Language - englishCOBISS.SI-ID - 16341849
Author
Eremita, Daniel |
Ilišević, Dijana
Topics
matematika |
algebra |
aditivnost |
kolobar |
prakolobar |
polprakolobar |
odvajanje |
posplošeno odvajanje |
homomorfizem |
antihomomorfizem |
algebra |
additivity |
ring |
prime ring |
semiprime ring |
derivation |
generalized derivation |
homomorphism |
anti-homomorphism
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Eremita, Daniel | 19550 |
Ilišević, Dijana |
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