Hemiring is a non-empty set which is equipped with the addition operation " " and the multiplication operation " " and satisfied four conditions, namely: is a commutative monoid with an identity element of , is semigroup, satisfied distributive properties the multiplication over addition on both sides, and satisfied for each . There are several types of hemiring such as idempotent hemiring, zerosumfree hemiring, simple hemiring and others. In this paper, it discusses the sufficient and

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... conditions of a hemiring that is said to be commutative and said to be simple, prove the characteristics of the operation in zerosumfree hemiring, idempotent hemiring, and simple hemiring.