I was just wondering if anybody knows of any good books or articles that study rings (and algebras) without (or not necessarily with) identity. I have gone through Thomas Hungerford's Algebra textbook (and loved it), but every book I have read afterwards on noncommutative algebra (Farb and Dennis' Noncommutative Algebra and T. Y. Lam's A First Course in Noncommutative Rings) have assumed that all rings are unitary. Could anyone give me a good reference please? Thank you all in advance!
$\begingroup$
$\endgroup$
Add a comment
|
2 Answers
$\begingroup$
$\endgroup$
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.
answered Apr 29, 2014 at 22:50
$\begingroup$
$\endgroup$
- Hungerford's Algebra
- Bresar's Introduction to Noncommutative Algebra.
- Behrens's Ring Theory.
- Warner's Modern Algebra (Section 32).
- Grove's Algebra (Chapter V).
- Herstein's Noncommutative Rings.
- McCoy's The Theory of Rings.
- Jacobson's Structure of Rings.
- Gardner and Wiegandt's Radical Theory of Rings.
