The lattice of idempotent distributive semiring varieties |
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Authors: | F Pastijn Yuqi Guo |
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Institution: | (1) Department of Mathematics, Statistics, and Computer Science, Marquette University, 53201-1881 Milwaukee, WI, USA;(2) Department of Mathematics, Yunnan University, 650091 Kunming, China |
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Abstract: | 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.
Project supported by the National Natural Science Foundation of China (Grant No. 19761004) and the Provincial Applied Fundamental
Research Foundation of Yunnan (96a001z). |
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Keywords: | idempotent semiring band distributive semiring variety |
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