on constant products of elements in skew polynomial rings

let $r$ be a reversible ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$ and $f(x)=a_0+a_1x+cdots+a_nx^n$ be a nonzero skew polynomial in $r[x;alpha]$. it is proved that if there exists a nonzero skew polynomial $g(x)=b_0+b_1x+cdots+b_mx^m$ in $r[x;alpha]$ such that $g(x)f(x)=c$ is a constant in $r$, then $b_0a_0=c$ and there exist nonzero elements $a$ and $r$ in $r$ such that $rf(x)=ac$. in particular, $r=ab_p$ for some $p$, $0leq pleq m$, and $a$ is either one or a product of at most $m$ coefficients from $f(x)$. furthermore, if $b_0$ is a unit in $r$, then $a_1,a_2,cdots, a_n$ are all nilpotent. as an application of the above result, it is proved that if $r$ is a weakly 2-primal ring which is $alpha$-compatible for an endomorphism $alpha$ of $r$, then a skew polynomial $f(x)$ in $r[x;alpha]$ is a unit if and only if its constant term is a unit in $r$ and other coefficients are all nilpotent.