Domain operations on semirings have been axiomatised in two different ways: by a map from an additively idempotent semiring into a boolean subalgebra of the semiring bounded by the additive and multiplicative unit of the semiring, or by an endofunction on a semiring that induces a distributive lattice bounded by the two units as its image. This note presents classes of semirings where these approaches coincide.

中文翻译：

---

域塞林斯联合

半环上的域操作已经以两种不同的方式公理化：通过从加幂半环到由半环的加法和乘法单元界定的半环的布尔子代数的映射，或者通过在半环上引入分配格的内函数以两个单位为界作为其图像。本笔记介绍了这些方法重合的半环类。