Necessary conditions for a semigroup ring to be an integral CRM-ring with identity

Abstract

The immersion of semigroup rings into division rings gave rise to Tamari's [6] hierarchical classification of semigroups. Some basic properties of this classification were given elsewhere ([1] , [2] and [3]), pointing out ([1], Remark 1) that Tamari's condition ([1], Theorem 1) is only a sufficient one. The present note continues Subbiah's [5] investigation of the necessity of Tamari's condition.