adjoin

adjoin (third-person singular simple present adjoins, present participle adjoining, simple past and past participle adjoined)

(transitive) To be in contact or connection with.
The living room and dining room adjoin each other.
- 2013, Graeme Simsion, The Rosie Project, →ISBN, page 55:
  We were in the living area, which adjoins the kitchen.
(transitive, mathematics, chiefly algebra and number theory) 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 $\mathbb {Q} [{\sqrt {2}}]$ can be obtained from $\mathbb {Q}$ by adjoining ${\sqrt {2}}$ to $\mathbb {Q}$ .

The field adjunction $\mathbb {Q} (\pi )$ can be obtained from $\mathbb {Q}$ by adjoining $\pi$ to $\mathbb {Q}$ .