Notes on $\left( {m,n} \right)$-ideals, III
Sándor Lajos · Proceedings of the Japan Academy Series A Mathematical Sciences · 1965
The first two papers of this series are 2 and 3.Let S be a semigroup.An (m, n)-ideal of S is called locally minimal if it contains no proper (m, n)-ideal.If a semigroup S contains no proper (m, n)-ideal, where m, n are arbitrary fixed positive integers, then by Theorem 4, S is a group.Thus we have the following result.Theorem 10.The locally minimal (m, n)-ideals of a semi-