Recent content by capsfan828

  1. C

    Is the Set of Units in a Ring with Identity a Subring?

    Homework Statement Prove or Disprove: The set of units in a ring R with identiy is a subring of R. Homework Equations The Attempt at a Solution Let S be the the set of units in a ring R with identity. For S to be a subring of R, 0R would have to be an element of S. Since S...
  2. C

    Congruence in Z(integers) mod n

    thanks for the response, much appreciated
  3. C

    Congruence in Z(integers) mod n

    Homework Statement In Z mod 5, compute (a + b)5. Homework Equations The Attempt at a Solution Noticing that (a+b)5 = a5+5(a4*b+2*a3*b2+2*a2*b3+a*b4)+b5. Since 5=0 in Z mod 5, it follows that 0(a4*b+2*a3*b2+2*a2*b3+a*b4)=0 and hence (a+b)5=a5+b5. I am just wondering if it...
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