A class of finite rings having one-sided zero divisors (Q810614)

Let R be a ring, let \(S_ 0\) and \(\Sigma\) denote the set of right zero divisors which are not left zero divisors and left identities which are not right identities, respectively. The author proves that if R is a finite ring then the following statements are equivalent: (i) \(S_ 0\neq 0\), \(R=\cup_{e\in \Sigma}eRe \cup eR(1-e),\) (ii) There exists a ring M such that R is isomorphic to a minimal right ideal A of M, and moreover, A has no identity and \(A^ 2\neq 0\).