On Commutativity of Prime Rings With (σ, τ)-Derivations
This work contains two sections. In the first section we tried to show that whether some commutativity properties, which are already satisfied in prime rings with ordinary derivations, are valid in prime rings with (σ, τ)-derivations. We see that some of those properties are satisfied in this case. So we give the generalizations of [6; Lemma 1, Lemma 2] and [5; Lemma 1] furthermore we proved some other properties and also we give a simple and short proof for a known property in prime rings (Lemma 1.6).
KeywordsCommutative Ring Prime Ring Short Proof Division Ring Polynomial Identity
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- 1.B. Felzenswalb, Derivation in prime rings, Proc. Amer. Math. Soc., Vol. 84. No. 1 (1982).Google Scholar
- 2.I. N. Herstein, Non commutative rings, The Math. Assoc. Amer. (1968).Google Scholar
- 3.Y. Hirano and H. Tominaga, Some commutativity theorems for prime rings with derivations and differentially semi prime rings, Math J. of Okayama Univ., Vol. 26 (1984).Google Scholar
- 4.W. S. Martindale, Prime rings satisfying general polynomial identity, J. of Algebra, Vol. 12 (1969).Google Scholar
- 5.J. H. Mayne, Ideals and centralizing mappings of prime rings, Proc. Amer. Math. Soc., Vol. 86 No. 2 (1982).Google Scholar
- 6.J.H. Mayne, Centralizing mappings of prime rings, Canada Math. Bui., Vol. 27(1) (1984).Google Scholar
- 7.E. C. Posner, Derivations in prime rings, Proc. Amer. Math. Soc., Vol. 8 No. 5 (1957).Google Scholar