Commutativity of prime rings with Symmetric Biderivations

descriptionPublicationkeyboard_double_arrow_right Article 01 Jan 2018 English Publisher:University of Zielona Góra, PolandJournal:Discussiones Mathematicae - General Algebra and Applications, volume 38, page 221 (issn: 1509-9415, eissn: 2084-0373,

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Authors: Reddy B. Ramoorthy; Reddy C. Jaya Subba;

doi: 10.7151/dmgaa.1297

Commutativity of prime rings with Symmetric Biderivations

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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.

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Yogi Vemana University
India

Keywords

prime ring, 16n60, commutativity and ideals, 16u80, 16w25, QA1-939, biderivation, Mathematics

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