Isomorphism theorems

Ring isomorphism theorems

The isomorphism theorems for rings are expressed as follows

First isomorphism theorem

Let be a ring homomorphism. Then the quotient by the kernel is isomorphic to the image: ring

Third isomorphism theorem

Let be ideals with . Then and ring

Fourth isomorphism theorem

Let be an ideal. Then the map

from subrngs containing to subrngs of is an order-preserving bijection. Moreover, is an ideal iff is.

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