Geodesic
Von Neumann regular skew-Laurent series rings
Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 565-568.

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Let $\varphi$ be an automorphism of finite order. Then the skew-Laurent series ring $A((x,\varphi))$ is von Neumann regular iff $A$ is semisimple Artinian. The third equivalent condition is that $A((x,\varphi))$ is semisimple Artinian. The same result for strong regularity is proved in the case of an arbitrary automorphism $\varphi$. 
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K. Sonin. Von Neumann regular skew-Laurent series rings. Fundamentalʹnaâ i prikladnaâ matematika, Tome 1 (1995) no. 2, pp. 565-568. http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a21/

[1] L. H. Rowen, Ring Theory, Academic Press, London, 1988 | MR

[2] K. R. Goodearl., Von Neumann Regular Rings, Pitman, London, 1979 | MR | Zbl

[3] K. I. Sonin., “Regulyarnye koltsa ryadov Lorana”, Fund. i prikl. mat., 1:1 (1995), 315–318 | MR