Glasnik matematički, Vol. 49 No. 2, 2014.
Izvorni znanstveni članak
https://doi.org/10.3336/gm.49.2.06
On some functional equations related to derivations and bicircular projections in rings
Maja Fošner
; Faculty of Logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Benjamin Marcen
; Faculty of Logistics, University of Maribor, Mariborska cesta 7, 3000 Celje, Slovenia
Nejc Širovnik
; Faculty of Natural Sciences and Mathematics, University of Maribor, Koroška cesta 160, 2000 Maribor, Slovenia
Joso Vukman
; Faculty of Mathematics, Natural Sciences and Information Technologies , University of Primorska, Glagoljaška 8, 6000 Koper and Institute of Mathematics, Physics and Mechanics, Jadranska 19, 1000 Ljubljana, Slovenia
Sažetak
In this paper we prove the following result. Let n≥ 1 be some fixed integer and let R be a prime ring with 2n < char(R) ≠ 2. Suppose there exist additive mappings S,T:R → R satisfying the relations
S(x2n)=S(x)x2n-1+xT(x)x2n-2+x2S(x)x2n-3+ ⋯ +x2n-1T(x),
T(x2n)=T(x)x2n-1+xS(x)x2n-2+ x2T(x)x2n-3+ ⋯ +x2n-1S(x)
for all x R. In this case S and T are of the form 2S(x)=D(x)+ζ (x), 2T(x)=D(x)-ζ (x) for all x R, where D:R → R is a derivation and ζ is an additive mapping, which maps R into its extended centroid. Besides, ζ (x2n)=0 for all x R. Functional equations related to bicircular projections are also investigated.
Ključne riječi
Derivation; functional identity; bicircular projection
Hrčak ID:
130886
URI
Datum izdavanja:
18.12.2014.
Posjeta: 515 *