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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     author = {K. Sonin},
     title = {Von {Neumann} regular {skew-Laurent} series rings},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {565--568},
     publisher = {mathdoc},
     volume = {1},
     number = {2},
     year = {1995},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_1995_1_2_a21/}
}
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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/