Books on Rings without Identity

Jacobson's Structure of rings develops a bit of ring theory without assuming identity. Also Gardner and Wiegandt's book Radical Theory of Rings does not assume identities.

Any book on $C^*$ algebras would also have to deal with rings missing identity.

1. Hungerford's Algebra
2. Bresar's Introduction to Noncommutative Algebra.
3. Behrens's Ring Theory.
4. Warner's Modern Algebra (Section 32).
5. Grove's Algebra (Chapter V).
6. Herstein's Noncommutative Rings.
7. McCoy's The Theory of Rings.
8. Jacobson's Structure of Rings.
9. Gardner and Wiegandt's Radical Theory of Rings.