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). (verb)
Examples of word adjoin
Abbey, and shew him the pastoral scenes that adjoin to it, the pure parent stream of Eden, and of Tweed, where Thomson first tuned his pastoral pipe, and I asked him to come to the Adelphi next day, to honour my sitting for the painting of my portrait.
The two football fields, which adjoin the hotel and belong to an adjacent middle school, are surrounded by substantial shrubs, and a black tarp, for good measure.
Then again, the guy in question has a few of the MN DNR high-and-mighty's in his pocket, so it's okay if he buys up 120 acres of state land (not federal, state) that adjoin his property, even though I haven't been able to find any records of that land being auctioned off ...
Touching on themes such as love, greed, poverty, joy, embarrassment and rivalry, Sophie's work is also on show on hoardings that adjoin Arlington House, the spectacularly brutal 1960s tower block outside the train station.
I work out where rooms adjoin, where storage space is partitioned off, which aspect the building will be facing … None of which has impact on larger pieces of the Story aspects, but which has the potential to dig me out of a brain-freeze if I should need assistance.