Define a new addition and multiplication on Q by a b = a + b+ 1 and a b = ab + a +b, where the operations on the right-hand side of the equal signs are ordinary addition, subtraction, and multiplication. Prove that, with the new operations, Q is a commutative ring with identity. Is it an integral domain.
Define a new addition and multiplication on Q by a b = a + b+ 1 and a b = ab + a +b, where the operations on the right-hand side of the equal signs are ordinary addition, subtraction, and multiplication. Prove that, with the new operations, Q is a commutative ring with identity. Is it an integral domain.
Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter5: Rings, Integral Domains, And Fields
Section5.1: Definition Of A Ring
Problem 32E: 32. Consider the set .
a. Construct addition and multiplication tables for, using the...
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![Define a new addition and multiplication on Q by
a b = a + b + 1 and a b = ab + a +b,
where the operations on the right-hand side of the equal signs are ordinary addition, subtraction, and
multiplication. Prove that, with the new operations, is a commutative ring with identity. Is it an
integral domain.](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F48baa9bc-98b9-4a36-81ee-4d15495d03a8%2F22caa9a3-34c9-4226-91ea-b2bd38e328a6%2F303rdb_processed.png&w=3840&q=75)
Transcribed Image Text:Define a new addition and multiplication on Q by
a b = a + b + 1 and a b = ab + a +b,
where the operations on the right-hand side of the equal signs are ordinary addition, subtraction, and
multiplication. Prove that, with the new operations, is a commutative ring with identity. Is it an
integral domain.
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