A definition of quotient ring of ring
Topics
About: ring
The table of contents of this article
Starting Context
- The reader knows a definition of ring.
- The reader knows a definition of ideal of ring.
Target Context
- The reader will have a definition of quotient ring of ring.
Orientation
There is a list of definitions discussed so far in this site.
There is a list of propositions discussed so far in this site.
Main Body
1: Definition
For any ring, \(S, +, \bullet\), its any both-sided ideal, I, and the equivalent relationship, \(\sim\), as \(p_1 \sim p_2\) if and only if \(p_1 - p_2 \in I\) for any \(p_1, p_2 \in S\), the set of equivalence classes, \(\{[p_\alpha]\}\), denoted as \(S/I\), with addition, +, as \([p_1] + [p_2] = [p_1 + p_2]\) and multiplication, \(\bullet\), as \([p_1] \bullet [p_2] = [p_1 \bullet p_2]\)
