Abstract.
The multiplicative reduct of an idempotent semiring with commutative addition is a regular band. Accordingly there are 13 distinct varieties consisting of idempotent semirings with commutative addition corresponding to the 13 subvarieties of the variety of regular bands. The lattice generated by the these 13 semiring varieties is described and models for the semirings free in these varieties are given.
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Received April 22, 2004; accepted in final form June 3, 2005.
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Pastijn, F., Zhao, X. Varieties of idempotent semirings with commutative addition. Algebra univers. 54, 301–321 (2005). https://doi.org/10.1007/s00012-005-1947-8
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DOI: https://doi.org/10.1007/s00012-005-1947-8