- #1

Artusartos

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I have a question about the proof that I attached...

1) Since R/I is not the zero ring, we know that [tex]1 \not= 0[/tex]. What is the reason to say [tex]1 + I \not= 0 + I[/tex] instead of [tex]1 \not= 0[/tex]?2) Also, how do we compute something like (a+I)(b+I)? Isn't this correct [tex](a+I)(b+I) = ab+aI+bI+I^2[/tex]?

3) Finally, if we have something like R/I, how do we know if the elements in R/I are of the form a+I or aI? Or is it both (since it's a ring)?

Thank you in advance

1) Since R/I is not the zero ring, we know that [tex]1 \not= 0[/tex]. What is the reason to say [tex]1 + I \not= 0 + I[/tex] instead of [tex]1 \not= 0[/tex]?2) Also, how do we compute something like (a+I)(b+I)? Isn't this correct [tex](a+I)(b+I) = ab+aI+bI+I^2[/tex]?

3) Finally, if we have something like R/I, how do we know if the elements in R/I are of the form a+I or aI? Or is it both (since it's a ring)?

Thank you in advance