Unibranch local ring

In commutative algebra, a **local ring** is a ring that has a unique maximal ideal. A **unibranch local ring** is a specific type of local ring characterized by the properties of its completion and its ramification properties. More formally, a local ring \( (R, \mathfrak{m}) \) is called a **unibranch local ring** if its closure in its completion is a domain that is unibranch.