Green's relations on a semiring satisfying additional identities xn≈x,(2n-1)x≈x,(x+y)n-1≈xn-1+yn-1 and(xy)n-1xn≈-1 xn-1yn-1 are studied.Equivalent characterizations of.(H)∧(H),(H)∧(B),(H)∨(B),(H)∨(B),(H)∨(D)and(H)∨(H)are obtained.The necessary and sufficient conditions for the above relations to be congruent are characterized,and then it is proved that the semiring classes determined by the above congruences are varieties.
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