Definition of "adjoin" in English

verb

1. (transitive) To be in contact or connection with.

   • The living room and dining room adjoin each other.

2. (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 #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;.
   • The field adjunction #92;mathbb#123;Q#125;(#92;pi) can be obtained from #92;mathbb#123;Q#125; by adjoining #92;pi to #92;mathbb#123;Q#125;.