ON GOLDIE PRIME IDEALS OF SKEW POLYNOMIAL RINGS

Let R be an associative ring with unity. For a semiprime Goldie ring R whit α:R→R a monomophism, we study on the Goldie prime ideals of the skew polynomial ring R[x;α]. In this paper we give a generalization of a result of Irving [4], and show that, if every strongly α-prime ideal of R is Goldie, then all prime ideals of the skew polynomial ring R[x;α] are left Goldoe.

Keywords:

polynomial near-ring , Baer near-ring , Armendariz-type ring , reduced ring