Idempotent distributive semirings II |
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Authors: | F. Pastijn |
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Affiliation: | 1. Dienst Hogere Meetkunde, Rijksuniversiteit te Gent, Krijgslaan 271, B-9000, Gent, Belgium
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Abstract: | In [2] it is shown that every idempotent distributive semiring is the P?onka sum of a semilattice ordered system of idempotent distributive semirings which satisfy the generalized absorption law x+xyx+x=x. We shall show that an idempotent distributive semiring which satisfies the above absorption law must be a subdirect product of a distributive lattice and a semiring which satisfies the additional identity xyx+x+xyx=xyx. Using this, we construct the lattice of all equational classes of idempotent distributive semirings for which the two reducts are normal bands. |
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