TITLE: Example of a ring without unity that has a subring with unity?
QUESTION [9 upvotes]: I can't think of a ring without unity that has a subring with unity. There must be some element in the parent ring that doesn't work with the subring's identity, but I'm struggling to see how that would be possible. Any suggestions?

REPLY [3 votes]: Any ring without a unit contains the zero ring, which is a ring with unity.