They conclude that "in many, maybe most, branches of ring theory the requirement of the existence of a unity element is not sensible, and therefore unacceptable."

Please ask the pro unity elements if they are really for somali unity, why don't the claim Djibouti, The 5th Ethiopian region and Kenyan NFD region as part and parcel of Greater Somalia.

If one omits the requirement that rings have a unity element, then subrings need only be non-empty and otherwise conform to the ring structure, and ideals become subrings.