Consider Q, the set of all rational numbers. For qâ??Q, q=m/n for m, n â?? Z. Suppose this is written in reduced form so gcd(m,n)=1. Let R â?? Q consist of all rational numbers for which the denominator of the reduced form is odd. Show that this set forms a ring under the usual operations of addition and multiplication.© BrainMass Inc. brainmass.com June 4, 2020, 12:44 am ad1c9bdddf
We need to check that:
1) R is closed under the operations of addition and multiplication:
Suppose, p=a/b and q=c/d belong to R. Then their product pq = (ac)/(bd), and the denominator (bd) is an odd number, since 2 is prime. Suppose, the ...
We show that rational numbers with an odd denominator form a ring.