On page 67 here -> http://www1.spms.ntu.edu.sg/~frederique/AA10.pdf
I understand why InJ is a subset of IJ right up to ax + ay is an element of IJ.
I figured that ax + ay = yx + xy (since a is in I and a is in J) so we have xy and yx are in IJ... but how do we know that when you add two elements of IJ, you still get an element of IJ... like, how do we know xy + xy is an element of IJ?
The first thing I would like to do is thank gummy_ratz for the notes. I'm currently studying this and the extra reference will be valuable. (Can't have too many textbooks! )
I'm sure tonio is correct in his analysis, however I have looked at page 62 and I have to admit defeat. What material on page 62 refers to the question??