> For the complete documentation index, see [llms.txt](https://adams-personal-organization.gitbook.io/compendium-of-predicates/llms.txt). Markdown versions of documentation pages are available by appending `.md` to page URLs; this page is available as [Markdown](https://adams-personal-organization.gitbook.io/compendium-of-predicates/definitions/algebra/boolean-ring.md).

# Boolean Ring

<details>

<summary><span class="math">\textbf{BooleanRing} \; A \; \otimes \; \oplus \; I \; U</span></summary>

***

$$\textbf{UnitRing} ; A ; \otimes ; \oplus ; I ; U$$

$$\textbf{Idempotent} ; A ; \otimes$$

***

```
pred BooleanRing(A: set univ, tms,pls: univ->univ->univ, I,U: univ) {
  UnitRing[A,tms,pls,I,U]
  Idempotent[A,tms]
}
```

</details>