nLab Boolean semiring

Disambiguation

In mathematics, the term Boolean semiring or Boolean rig can refer to:

• Boolean semiring (Bartels), a rig satisfying $x^2 = x$
• Boolean semiring (Guzmán), a rig satisfying $x^2 = x$ and $1 + x + x = 1$
• One also has rigs satisfying $x^2 = x$ and $x + x = 0$, but those rigs are provably equivalent to Boolean rings.

The term Boolean semiring can also refer to the following:

• Boolean semiring (Chajda & Kotrle)
• Boolean semiring (Guterman)?
• Boolean semiring (Subrahmanyam)?

References

For the fact that “Boolean semiring” is used for multiple inequivalent structures in mathematics:

• Morgan Rogers, From free idempotent monoids to free multiplicatively idempotent rigs [arXiv:2408.17440]

• J-B Vienney, Are Boolean rigs commutative?, Category theory Zulip, (web)

category: disambiguation