ON SUM ANNIHILATOR IDEALS IN ORE EXTENSIONS

A ring $R$ is called a left Ikeda-Nakayama (left IN-ring) if the right annihilator of intersection any two ideals sum annihilators. As generalization IN-rings, SA-ring annihilators an ideal $R$. It natural to ask IN and SA property can be extended from $R[x; \alpha, \delta]$. In this note, results concerning conditions will allow these properties transfer skew polynomials $R[x;\alpha,\delta]$ are obtained. addition, for $(\alpha,\delta)$-compatible $R$, it shown that: (i) If $S = R[x;\alpha,\delta]$ IN-ring with ${\rm{Idm}}(R) ={\rm{Idm}}(R[x;\alpha, \delta])$, then McCoy. (ii) Every reduced finitely many minimal prime semiprime Goldie ring. (iii) commutative principal (PIR) so $R[x]$. (iv) $n$ positive integer, only $R[x]/(x^{n+1})$ SA.