On (anti-)multiplicative generalized derivations

Daniel Eremita (Author), Dijana Ilišević (Author)

Abstract

Naj 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 ▫$I$▫.

Keywords

matematika;algebra;aditivnost;kolobar;prakolobar;polprakolobar;odvajanje;posplošeno odvajanje;homomorfizem;antihomomorfizem;additivity;ring;prime ring;semiprime ring;derivation;generalized derivation;homomorphism;anti-homomorphism;

Data

Language:	English
Year of publishing:	2012
Typology:	1.01 - Original Scientific Article
Organization:	UM FNM - Faculty of Natural Sciences and Mathematics
UDC:	512.552
COBISS:	16341849
ISSN:	0017-095X
Views:	36
Downloads:	21
Average score:	0 (0 votes)
Metadata:

Other data

Secondary language:	Slovenian
Secondary title:	O (anti)multiplikativnih posplošenih odvajanjih
Secondary abstract:	Let ▫$R$▫ be a semiprime ring and let ▫$F, f \colon R \to R$▫ be (not necessarily additive) maps satisfying ▫$F(xy) = F(x)y + xf(y)$▫ for all ▫$x,y \in R$▫. Suppose that there are integers ▫$m$▫ and ▫$n$▫ such that ▫$F(uv) = mF(u)F(v) + nF(v)F(u)$▫ for all ▫$u$▫, ▫$v$▫ in some nonzero ideal ▫$I$▫ of ▫$R$▫. Under some mild assumptions on ▫$R$▫, we prove that there exists ▫$c \in C(I^{\bot\bot})$▫ such that ▫$c = (m+n)c^2$▫, ▫$nc[I^{\bot\bot}, I^{\bot\bot}] = 0$▫ and ▫$F(x) = cx$▫ for all ▫$x \in I^{\bot\bot}$▫. The main result is then applied to the case when ▫$F$▫ is multiplicative or anti-multiplicative on ▫$I$▫.
Secondary keywords:	matematika;algebra;aditivnost;kolobar;prakolobar;polprakolobar;odvajanje;posplošeno odvajanje;homomorfizem;antihomomorfizem;
URN:	URN:SI:UM:
Type (COBISS):	Not categorized
Pages:	str. 105-118
Volume:	Vol. 47
Issue:	no. 1
Chronology:	2012
ID:	1476631