ON ZERO-DIVISORS IN SKEW INVERSE LAURENT SERIES OVER NONCOMMUTATIVE RINGS

In the present note, we continue to study zero-divisor properties of general skew inverse Laurent series rings R((x(-1); sigma, delta)), where R is an associative ring equipped with an automorphism sigma and a sigma-derivation delta. Extending the results of a large number of papers on the McCoy property for ordinary and skew polynomial rings, we study a version of the McCoy property for general skew inverse Laurent series extensions. We obtain some necessary or sufficient conditions for a ring to be (sigma, delta)-SILS McCoy and prove that this property is preserved under a number of ring extensions. In particular, it passes to certain subrings of the (skew-)upper triangular matrix rings. In relation with this work and as an application of (sigma, delta)-SILS McCoy rings, we investigate the interplay between the ring-theoretical properties of a general skew inverse Laurent series ring R((x(-1); sigma, delta)) and the graph-theoretical properties of its zero-divisor graph (Gamma) over bar (R((x(-1); sigma, delta))).