The McCoy Condition on Skew Polynomial Rings

Zero Divisors in Skew Power Series Rings

“…Then R is a domain, and so R is -skew power-serieswise McCoy by Corollary 3.3(1). But, for any odd prime integer q, the ring R/qR q q q q cannot be¯ -skew power-serieswise McCoy by the same argument as in [4,Example 11]. …”

“…Notice that Mat n R and U n R over any ring R are not -skew powerserieswise McCoy by help of [4,Example 11]. where p ij ∈ R x for any i j.…”

“…(2) If R is -skew power-serieswise Armendariz, then a is i b ju = 0 for any i s j u from PQ = 0 above, and so f i¯ i g j = 0, proving that R x is¯ -skew powerserieswise Armendariz. Downloaded by [OARE Consortium] at 13:03 07 July 2015 (3) We apply the proof of [4,Theorem 20]. Suppose that R is -skew powerserieswise McCoy and p y = 0 and q y = 0 above.…”

“…A ring R is called -skew McCoy [4,Defiition 1] if for any nonzero polynomials p x and q x ∈ R x , p x q x = 0 implies p x c = 0 for some nonzero c ∈ R. Any -skew Armendariz ring is -skew McCoy by [4,Proposition 2(1)]. Downloaded by [OARE Consortium] at 13:03 07 July 2015…”

“…The ring R is called a -skew power-serieswise McCoy if for any nonzero p x and q x ∈ R x , p x q x = 0 implies p x c = 0 for some nonzero c ∈ R.Every -skew power-serieswise McCoy rings is clearly -skew McCoy, butMcCoy rings need not -skew power-serieswise McCoy by[4, Example 4].…”