adjoineth

Verb

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

1. (ambitransitive) 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.
2. (transitive) 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 #92;mathbb#123;Q#125;#91;#92;sqrt#123;2#125;#93; can be obtained from #92;mathbb#123;Q#125; by adjoining #92;sqrt#123;2#125; to #92;mathbb#123;Q#125;.