adjoin

verb2

1. •
   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.
   • It's at this point that these three neighbourhoods adjoin.
2. •
   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.