论文信息 - EXTENSIONS OF McCOY'S THEOREM

EXTENSIONS OF McCOY'S THEOREM

Abstract McCoy proved that for a right ideal A of S = R[x1, . . ., xk] over a ring R, if rS(A) ≠ 0 then rR(A) ≠ 0. We extend the result to the Ore extensions, the skew monoid rings and the skew power series rings over non-commutative rings and so on.

Yang Lee | N. Kim | C. Hong

[1] Pace P. Nielsen. Semi-commutativity and the McCoy condition , 2006 .

[2] Y. Hirano. On annihilator ideals of a polynomial ring over a noncommutative ring , 2002 .

[3] D. Passman,et al. The algebraic structure of group rings , 1977 .

[4] R. Gilmer,et al. Zero divisors in power series rings. , 1975 .

[5] D. E. Fields. Zero divisors and nilpotent elements in power series rings , 1971 .

[6] N. McCoy. Annihilators in Polynomial Rings , 1957 .

[7] Neal H. McCoy,et al. Remarks on Divisors of Zero , 1942 .