A note centralizers in semiprime rings

• Autorzy: Kosi-Ulbl I.
• Języki publikacji: EN

Abstrakty

EN

The purpose of this paper is to prove the following result: Let R be a (m+n + 2)! and 3m2n + 3mn2 + 4m2 + 4n2 +10mn-torsion free semiprime ring with an identity element and let T : R -R be an additive mapping such that 3T(xm+n+1) = T(x)xm+n + xmT(x)xn + xm=nT(x) is fulfilled for all x is an element R and some fixed nonnegative integers m and n, m+n=0. In this case T is a centralizer.

Słowa kluczowe

EN

prime ring; semiprime ring; centralizer; centralizator Jordana; left (right) centralizer

PL

pierścienie pierwsze; centralizator; centralizator Jordana

• Wydawca: De Gruyter
• Czasopismo: Demonstratio Mathematica
• Rocznik: 2005
• Tom: Vol. 38, nr 2
• Strony: 277--282
• Opis fizyczny: Bibliogr. 8 poz.

Twórcy

autor

Kosi-Ulbl I.

• Department of Mathematics, University of Maribor, PEF, Koroska 160, 2000 Maribor, Slovenia

Bibliografia

• [1] M. Brešar, Jordan derivations on semiprime rings, Proc. Amer., Math. Soc. 104 (1988), 1003-1006.
• [2] M. Brešar and J. Vukman, Jordan derivations on prime rings, Bull. Austral. Math. Soc. 3 (1988), 321-322.
• [3] J. Cusack, Jordan derivations on rings, Proc. Amer. Math. Soc. 53 (1975), 321-324.
• [4] I. N. Herstein, Jordan derivations of prime rings, Proc. Amer. Math. Soc. 8 (1957), 1104-1110.
• [5] J. Vukman, An identity related to centralizers in semiprime rings, Comment. Math. Univ. Carolinae 40 (1999), 447-456. ·
• [6] J. Vukman, Centralizers of semiprime rings, Comment. Math. Univ. Carolinae, 42, 2(2001), 237-245.
• [7] J. Vukman and I. Kosi-Ulbl, An equation related to centralizers in semiprime rings, Glasnik Mat. Vol. 38 (58) (2003), 253-261.
• [8] B. Zalar, On centralizers of semiprime rings, Comment. Math. Univ. Carolinae 32 (1991), 609-614.