verb To share a common boundary or border with; to be physically contiguous to (a piece of land or property).
The living room and dining room adjoin each other.
verb To extend an algebraic object (e.g. a field, a ring, etc.) by adding to it an element not belonging to it and then ensuring closure, for example by also adding all finite power series of the element.
The ring adjunction ℚ[2] can be obtained from ℚ by adjoining 2 to ℚ.