ON LEFT α-MULTIPLIERS AND COMMUTATIVITY OF SEMIPRIME RINGS
2
조회
0
다운로드
0
인용
0
참고문헌
키워드
초록
Let R be a ring, and α be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left α-multiplier (centralizer) if H(xy) = H(x)α(y) holds for all x,y ∈ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left α-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.
Abstract
Let R be a ring, and α be an endomorphism of R. An additive mapping H : R ${\rightarrow}$ R is called a left α-multiplier (centralizer) if H(xy) = H(x)α(y) holds for all x,y ∈ R. In this paper, we shall investigate the commutativity of prime and semiprime rings admitting left α-multiplier satisfying any one of the properties: (i) H([x,y])-[x,y] = 0, (ii) H([x,y])+[x,y] = 0, (iii) $H(x{\circ}y)-x{\circ}y=0$, (iv) $H(x{\circ}y)+x{\circ}y=0$, (v) H(xy) = xy, (vi) H(xy) = yx, (vii) $H(x^2)=x^2$, (viii) $H(x^2)=-x^2$ for all x, y in some appropriate subset of R.
참고문헌 (13)
- E. Albash, "On -centralizers of semiprime rings", Siberian Math. J, 48(2), pp.191~196 (2007)
- S. Ali, "Jordan -centralizers in rings and some applications", Bol. Soc. Paran. Math, 26(1-2), pp.71~80 (2008)
- F. W. Anderson, "Lectures on noncommutative rings" (2002), Univ. of Oregon
- M. Ashraf, "On left multipliers and the commutativity of prime rings", Demon- stratio Math, 41(4), pp.763~771 (2008)
- M. Ashraf, "On derivations in rings and their applications", Aligarh Bull. Math, 25(2), pp.79~107 (2006)
- M. Bresar, "On the distance of the composition of two derivations to the generalized derivations", Glasgow Math. J, 33(1), pp.89~93 (1991)
- W. Cortes, "On Lie ideals and left Jordan -centralizers of 2-torsion- free rings", Math. J. Okayama Univ, 51, pp.111~119 (2009)
- M. N. Daif, "On -centralizers of semiprime rings (II)", St. Petersburg Math. J, 21(1), pp.43~52 (2010)
- I. N. Herstein, "Rings with Involution" (1976), University of Chicago Press
- M. A. Quadri, "Generalized derivations and commutativity of prime rings", Indian J. Pure Appl. Math, 34(9), pp.1393~1396 (2003)
- J. Vukman, "On centralizers of semiprime rings", Aequationes Math, 66(3), pp.277~283 (2003)
- J. Vukman, "On centralizers of semiprime rings with involution", Studia Sci. Math. Hungar, 43(1), pp.61~67 (2006)
- B. Zalar, "On centralizers of semiprime rings", Comment. Math. Univ. Carolin, 32(4), pp.609~614 (1991)