# Ideal and factor rings

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Please if you are going to solve this problem please be very accurate!! (and careful!!). I have used brainmass before and have recieved incorrect answers on mulitple occations (answers that initially seemed correct) and it has hindered my studying. I have decided to give it another chance. With that said, thank you very much for viewing my problem. I welcome any comments or concerns.

Problem:

Note: | | is suppose to denote a matrix

If R =

|S S|

|0 S|

and A =

|0 S|

|0 0|

, S any ring, show that A is an ideal of R and describe the cosets in R/A

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