11. In group theory and ring theory , brackets denote the commutator. 12. Some theorems of ring theory are false for rngs. 13. Hence such things as group theory and ring theory took their places in pure mathematics. 14. And of course that they don t want my Quantum Ring Theory as an opponent. 15. In simpler terms, consider the examples of finite group theory, field theory and ring theory . 16. He created the well-known economic theory regarding skill complementarities called Kremer's O-Ring Theory of Economic Development. 17. See also glossary of commutative algebra, glossary of classical algebraic geometry, and glossary of ring theory . 18. In ring theory , a subring which is ideal. 19. *Open any book you have on ring theory and find references ( author + page number )! 20. The definitions of terms used throughout ring theory may be found in the glossary of ring theory.