Results 21 to 30 of about 205 (52)
A remark on centralizers in semiprime rings [PDF]
, 2004 The purpose of this paper is to prove the following result: Let m 1, n 1 be fixed integers and let R be a (m + n + 2)!-torsion free semiprime ring with the identity element. Suppose there exists an additive mapping T : R R, such that T(xm+n+1) = xm T(x)
Irena Kosi-Ulbl
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On derivations and commutativity in prime rings
International Journal of Mathematics and Mathematical Sciences, Volume 2004, Issue 70, Page 3859-3865, 2004., 2004 Let R be a prime ring of characteristic different from 2, d a nonzero derivation of R, and I a nonzero right ideal of R such that [[d(x), x], [d(y), y]] = 0, for all x, y ∈ I. We prove that if [I, I]I ≠ 0, then d(I)I = 0.
Vincenzo De Filippis
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On Commutativity of Rings with Generalized Derivations [PDF]
, 2002 The concept of derivations as well as of generalized inner derivations have been generalized as an additive function F : R → R satisfying F(xy) = F(x)y + xd(y) for all x, y ∈ R, where d is a derivation on R, such a function F is said to be a ...
Rehman, Nadeem ur
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On zero subrings and periodic subrings
International Journal of Mathematics and Mathematical Sciences, Volume 28, Issue 7, Page 413-417, 2001., 2001 We give new proofs of two theorems on rings in which every zero subring is finite; and we apply these theorems to obtain a necessary and sufficient condition for an infinite ring with periodic additive group to have an infinite periodic subring.
Howard E. Bell
wiley +1 more source
Identities with derivations on rings and Banach algebras [PDF]
, 2005 In this paper we prove the following result. Let m 1, n 1 be integers and let R be a 2mn(m+n-1)!-torsion free semiprime ring. Suppose there exist derivations D, G : R R such that D(xm)xn + xnG(xm) = 0 holds for all x R.
Joso Vukman
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International Journal of Mathematics and Mathematical Sciences, Volume 24, Issue 1, Page 55-57, 2000., 2000 For prime rings R, we characterize the set U∩CR([U, U]), where U is a right ideal of R; and we apply our result to obtain a commutativity‐or‐finiteness theorem. We include extensions to semiprime rings.
Howard E. Bell
wiley +1 more source
Derivations of higher order in semiprime rings
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 1, Page 89-92, 1998., 1997 Let R be a 2‐torsion free semiprime ring with derivation d. Supposed d2n is a derivation of R, where n is a positive integer. It is shown that if R is (4n − 2)‐torsion free or if R is an inner derivation of R, then d2n−1 = 0.
Jiang Luh, Youpei Ye
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Commutativity results for semiprime rings with derivations
International Journal of Mathematics and Mathematical Sciences, Volume 21, Issue 3, Page 471-474, 1998., 1996 We extend a result of Herstein concerning a derivation d on a prime ring R satisfying [d(x), d(y)] = 0 for all x, y ∈ R, to the case of semiprime rings. An extension of this result is proved for a two‐sided ideal but is shown to be not true for a one‐sided ideal.
Mohammad Nagy Daif
wiley +1 more source
PRIME, MAXIMAL AND PRIMITIVE IDEALS IN SOME SUBRINGS OF POLYNOMIAL RINGS [PDF]
, 2014 In this paper we describe prime, maximal and primitive ideals in some graded subrings of polynomial rings.
Ferrero, Miguel, Miranda, Edilson Soares
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International Journal of Mathematics and Mathematical Sciences, Volume 20, Issue 2, Page 263-266, 1997., 1995 Let R be a ring A bi‐additive symmetric mapping d : R × R → R is called a symmetric bi‐derivation if, for any fixed y ∈ R, the mapping x → D(x, y) is a derivation. The purpose of this paper is to prove the following conjecture of Vukman. Let R be a noncommutative prime ring with suitable characteristic restrictions, and let D : R × R → R and f : x → D ...
Qing Deng
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