Consider the sets Z, R, Z5, Z4 and SL2(R) with the operations of addition and multiplication. For each of the following, give a brief explanation of your answer (does not need to be a full proof).

(a) Which of these sets are rings? (b) Which of these sets are fields? (c) Which of these sets are integral domains?

My answer:

Z:ring. integral domian

not field becasue the only non zero integer that have multiplaication inverse are 1 and -1

R:ring, field, integral domain

Z5:ring, field, integral domain

Z4:ring, field

not integral domain because [2][2]=[0]

SL2(R) i only know it is not integral domain