The lattice of idempotent distributive semiring varieties

A solution is given for the word problem for free idempotent distributive semirings. Using this solution the latticeL (ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out thatL (ID) is isomorphic to the direct product of a four-element lattice and a...

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Veröffentlicht in:Science China. Mathematics 1999-08, Vol.42 (8), p.785-804
Hauptverfasser: Pastijn, F., Guo, Yuqi
Format: Artikel
Sprache:eng
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Zusammenfassung:A solution is given for the word problem for free idempotent distributive semirings. Using this solution the latticeL (ID) of subvarieties of the variety ID of idempotent distributive semirings is determined. It turns out thatL (ID) is isomorphic to the direct product of a four-element lattice and a lattice which is itself a subdirect product of four copies of the latticeL(B) of all band varieties. ThereforeL(ID) is countably infinite and distributive. Every subvariety of ID is finitely based.
ISSN:1006-9283
1674-7283
1862-2763
1869-1862
DOI:10.1007/BF02884266