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Idempotent semirings with a commutative additive reduct

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Abstract

For every semigroup S , we define a congruence relation ρ on the power semiring (P(S),\cup,\circ) of S . If S is a band, then P(S)/ρ is an idempotent semiring . This enables us to find models for the free objects in the variety of idempotent semiring s whose additive reduct is a semilattice.

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  1. Department of Mathematics, North West University, 710069, Xian, Shaanxi, China

    Xianzhong Zhao

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  1. Xianzhong Zhao
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Correspondence to Xianzhong Zhao.

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Communicated by F. Pastijn

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Zhao, X. Idempotent semirings with a commutative additive reduct. Semigroup Forum 64, 289–296 (2002). https://doi.org/10.1007/s002330010048

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  • DOI: https://doi.org/10.1007/s002330010048

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