Open Accessσ- ideals and generalized derivations in σ-prime rings
Author(s) -
Mohd Rais Khan,
Deepa Arora,
M. Ali Khan
Publication year - 2013
Publication title -
boletim da sociedade paranaense de matemática
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.347
H-Index - 15
eISSN - 2175-1188
pISSN - 0037-8712
DOI - 10.5269/bspm.v31i2.12119
Subject(s) - prime (order theory) , mathematics , commutative property , prime ring , commutative ring , ring (chemistry) , combinatorics , pure mathematics , chemistry , organic chemistry
Let R be a prime ring and F and G be generalized derivations of R with associated derivations d and g respectively. In the present paper, we shall investigate the commutativity of R admitting generalized derivations F and G satisfying any one of the properties: (i) F(x)x = x G(x), (ii) F(x2) = x2 , (iii) [F(x), y] = [x, G(y)], (iv) d(x)F(y) = xy, (v) F([x, y]) = [F(x), y] + [d(y), x] and (vi) F(x ◦ y) = F(x) ◦ y − d(y) ◦ x for all x, y in some appropriate subset of R
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