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Vanilla 1.1.10 is a product of Lussumo. More Information: Documentation, Community Support.

1. Added some remark on the order of a semiring. Actually, does anybody know if any semiring embedds into a semifield?

• CommentRowNumber2.
• CommentAuthorTodd_Trimble
• CommentTimeNov 12th 2018

Fixed the proof of the join property; added an observation about the example of languages.

• CommentRowNumber3.
• CommentAuthorTodd_Trimble
• CommentTimeNov 12th 2018

Seems a distributive lattice is a semiring; if a semifield is a semiring where multiplication by a non-zero $x$ is invertible, then $x \wedge x = x \wedge \top$ implies $x = \top$ assuming embeddability in a semifield. So, the answer is no.

• CommentRowNumber4.
• CommentAuthorDavidRoberts
• CommentTimeNov 12th 2018

Connes and Consani, for instance, say a semifield is a semiring (ie a rig) where the nonzero elements are all invertible.

2. Corrected typo (“concatentation” for “concatenation”).

Anonymous

• CommentRowNumber6.
• CommentAuthorTim_Porter
• CommentTimeSep 8th 2021