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Pregled bibliografske jedinice broj: 587626

On (anti-)multiplicative generalized derivations


Eremita, Daniel; Ilišević, Dijana
On (anti-)multiplicative generalized derivations // Glasnik Matematicki, 47(67) (2012), 1; 105-118 (međunarodna recenzija, članak, znanstveni)


Naslov
On (anti-)multiplicative generalized derivations

Autori
Eremita, Daniel ; Ilišević, Dijana

Izvornik
Glasnik Matematicki (0017-095X) 47(67) (2012), 1; 105-118

Vrsta, podvrsta i kategorija rada
Radovi u časopisima, članak, znanstveni

Ključne riječi
Additivity; ring; semiprime ring; prime ring; derivation; generalized derivation; homomorphism; anti-homomorphism

Sažetak
Let $R$ be a semiprime ring and let $F, f : R \to R$ 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 $c \in C(I^{;\perp \perp};)$ such that $c=(m+n)c^2, $ $nc[I^{;\perp \perp};, I^{;\perp \perp};]=0$ and $F(x)=cx$ for all $x \in I^{;\perp \perp};.$ The main result is then applied to the case when $F$ is multiplicative or anti-multiplicative on $I.$

Izvorni jezik
Engleski

Znanstvena područja
Matematika



POVEZANOST RADA


Projekt / tema
037-0372784-2757 - Preslikavanja na modulima nad prstenima, apstraktnim i operatorskim algebrama (Dijana Ilišević, )

Ustanove
Prirodoslovno-matematički fakultet, Zagreb

Autor s matičnim brojem:
Dijana Ilišević, (228992)

Časopis indeksira:


  • Web of Science Core Collection (WoSCC)
    • Science Citation Index Expanded (SCI-EXP)
    • SCI-EXP, SSCI i/ili A&HCI
  • Scopus


Uključenost u ostale bibliografske baze podataka:


  • MathSciNet
  • Zentrallblatt für Mathematik/Mathematical Abstracts