Define addition and multiplication, denoted by and , respectively, on the set Q as follows For a, b Q, a b a b 7, a b a b (ab 1) (a) Prove that (Q, , ) is a ring, (b) Is this ring commutative (c) Does the ring have a unity What about units (d) Is this ring an integral domain a field txy rta

Question: Define addition and multiplication, denoted by and , respectively, on the set Q as follows. For a, b Q, a b= a

Define addition and multiplication, denoted by Š• and Š™, respectively, on the set Q as follows. For a, b ˆˆ Q, a Š• b=

a + b + 7, a Š™ b = a + b + (ab/1). (a) Prove that (Q, Š•, Š™) is a ring, (b) Is this ring commutative? (c) Does the ring have a unity? What about units? (d) Is this ring an integral domain? a field?

txy //rta

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a We shall verify one of the distributive laws If o 6 c Q then A b c a b c 7 a b c 7 ab c 77 a b c 7 ... View full answer

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