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.

Subgrpous

Prove: any subgroup of the order of p^(n-1) in a group of order p^n, where p is a prime, is a normal subgroup

Integral domain

There is integral domain with exactly six elements. Disprove or Prove

Algebraic numbers

Is sin 1 degree an algebraic number?

Transformations in Hom(v,v)

Prove that the invertible transformations in Hom(v,v) form a group under multiplication

Automorphism

1. Let T be any automorphism of G, show that ZT<(subset) Z. If G is a group and Z is the center of G.