The properties of medial and their related idempotents in r-wide semigroups are discussed.Based on this,we proved that r-wide semigroups with a weakly type A multiplicative medial idempotent u are naturally ordered r-wide semigroups anduis a maximum idempotent.
r-wide semigroupsmedial idempotentsnaturally orderweakly type A s-emigroups
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