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- W2000709219 abstract "In [8] the author studied the question of the primitivity of an Ore extension R [ x , δ], where δ is a derivation of the ring R . If a is an automorphism of R then it can be shown that R [ x , α] is primitive if the following conditions are satisfied: (i) no power α s S ≥ 1, of α is inner; (ii) the only ideals of R invariant under α are 0 and R . These conditions are also known to be necessary and sufficient for the skew Laurent polynomial ring R [ x , x −1 , α] to be simple [9]. The object of this paper is to find conditions which are sufficient for R [ x , x −1 , α] to be primitive. The results obtained are remarkably similar to those of [8]. Two logically independent conditions are each found to be sufficient for the primitivity of R [ x , x −1 , α]. Of these, one is also shown to be sufficient for R [ x , α] to be primitive. Included in the examples illustrating these results are some applications to the theory of primitive group rings. The basic techniques involved are also applied to produce a counterexample to the converse of a theorem of Goldie and Michler [3] on when R [ x , x −1 , α] is a Jacobson ring." @default.
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- W2000709219 date "1978-01-01" @default.
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- W2000709219 title "Primitive skew Laurent polynomial rings" @default.
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- W2000709219 doi "https://doi.org/10.1017/s0017089500003414" @default.
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