Unformatted text preview: containing M are M and R . Recall that a ring is called simple if it has no ideals other than the trivial ideal f g and the whole ring; so a nonzero ring is simple precisely when f g is a maximal ideal. Proposition 6.3.12. A proper ideal M in R is maximal if, and only if, R=M is simple. Proof. Exercise 6.3.6 . n Proposition 6.3.13. A (nonzero) commutative ring R with multiplicative identity is a ﬁeld if, and only if, R is simple....
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- Fall '08
- Algebra, Homomorphism, Epimorphism, Diamond Isomorphism Theorem