This is an unformatted preview. Please download the attached document for the or

This is an unformatted preview. Please download the attached document for the original format.Shawn Hicks California State University Fullerton Math 407 Edited by: Veronica Holbrook April 7 2014 Spring 2014 Solutions to Homework 7 Quotient Structures 1. If R is a ring and I is a subgroup of R (under addition) then I is an ideal if rx xr I for all r R and for all x I . Dene R/I = {r + I | r R}. Prove that R/I is a ring under the operations (r + I ) + (s + I ) = (r + s) + I and (r + I ) (s + I ) = rs + I for r s R. Recall that you must show that each operation is well-dened that is if you choose dierent representatives for the cosets then the sum and product do not change.

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