COMMUTATIVITY OF PRIME RINGS WITH SYMMETRIC BIDERIVATIONS
Journal Title: Discussiones Mathematicae - General Algebra and Applications - Year 2018, Vol 38, Issue 2
Abstract
The present paper shows some results on the commutativity of R: Let R be a prime ring and for any nonzero ideal I of R, if R admits a biderivation B such that it satisfies any one of the following properties (i) B([x, y], z) = [x, y], (ii) B([x, y], m) + [x, y] = 0, (iii) B(xoy, z) = xoy, (iv) B(xoy, z) + xoy = 0, (v) B(x, y)oB(y, z) = 0, (vi)B(x, y)oB(y, z) = xoz, (vii) B(x, y)oB(y, z) + xoy = 0, for all x, y, z ∈ R, then R is a commutative ring. Keywords: prime ring, biderivation, commutativity and ideals. 2010 Mathematics Subject Classification: 16W25, 16N60, 16U80
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