To extend an algebraic object (e.g. a field, a ring, etc.) by adding to it (an element not belonging to it) and all finite power series of (the element)
\textbf{Q}\left(\sqrt{2}\right) can be obtained from \textbf{Q} by adjoining \sqrt{2} to \textbf{Q}.
If one room, place, or object adjoins another, they are next to each other. a room, building, or piece of land that adjoins something is next to it and connected to it (adjoindre, from adjungere, from ad- + jungere )