rings

Please, if you are going to answer this question, include as much detail as you can so that I can follow what your doing. Thank you very much! In Zn x Zm (integers modulo n and m respectively) find the characteristic of the ring please.

rings

If e^2 = e, show that (1-e)re and er(1-e) are nilpotents for all r belonging to R. ALSO, if e^2 = e, show that e+(1-e)re and e+er(1-e) are idempotents for all r belonging to R

rings: integral domains and fields

Please, if you are going to answer this question, include as much detail as you can so that I can follow what your doing. Thank you very much! Find all the roots of x^2 + 3x - 4 in Z (integers) AND Z6 (integers modulo 6) AND Z4 (integers modulo 4)

Euclidean group

The problem has been better defined. please help.

Group Action

The problem has been better defined. please help.