Iranian Journal of

In this paper, we investigate various kinds of extensions of twin-good rings. Moreover, we prove that every element of an abelian neat ring R is twin-good if and only if R has no factor ring isomorphic to‌ $Z_2$ or $Z_3$. The main result of [24] states some conditions that any right self-injective ring R is twin-good. We extend this result to any regular Baer ring R by proving that every element of a regular Baer ring is twin-good if and only if R has no factor ring isomorphic to  $Z_2$ or $Z_3$. Also we illustrate conditions under which extending modules, continuous modules and some classes of vector space are twin-good.