MATH 668 Midterm: MATH 668 Louisville 668S16E1

• School: UofL
• Department: Mathematics
• Course: MATH 668
• Professor: All

Document Summary

Here s is a subring of r because it is closed under addition, multiplication, and additive inverses. Considering a d = ad+bc bd , whose denominator is not divisible by 3; likewise a bd , which has the same denominator, b and a. Addendum: note that the fact that 3 is prime is critical here; if we were to use, say, divisibility. 6, there would be a real problem in that 1. 3 would be in the putative ring while their product is not. , which again is in s since b is not divisible by 3. + c c numbers a and b. (b) r is the ring of all real 2 2 matrices; s is the set of all matrices of the form [ a. Multiplicative closure takes a bit more work: [ a. Addition and additive inverses are clearly closed: [ a and [ a.