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Math and science::Algebra::Aluffi

Rings. Third isomorphism theorem, an example.

Let a,b∈R be elements in a commutative ring R. Use (b¯) to denote the equivalence class of b in R/(a). Then firstly we have:

[(b¯)=?(a)]
<p>and with that result it can be seen that:</p>
[ R/(a)(b¯)≅?]

Recap of ring generators:

Ring generators

Let a∈R be an element of a ring. The subset Ra is a left-ideal and the subset aR is a right-ideal. If R is a commutative ring, the ideals coincide, and the syntax (a) is used to denote the ideal.