The authors enumerate all semirings of order at most 6 (and some classes up to order 8), giving exact counts up to isomorphism and up to isomorphism or anti-isomorphism.
Cube-Based Isomorph-Free Finite Model Finding
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Counting finite semirings
The authors enumerate all semirings of order at most 6 (and some classes up to order 8), giving exact counts up to isomorphism and up to isomorphism or anti-isomorphism.