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Finding the relation between ring and mod integers

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R is the set of integers mod 7 under the addition and multiplication mod 7.
That is, the elements of R are the seven symbols 0^,1^,2^,3^,4^,5^,6^
where
(1) I^+j^=k^ where k is the remainder of I + j on division by 7
(thus for instance, 4^+5^=2^ since 4 + 5 = 9 , which when divided by 7
leaves remainder of 2)
(2) i^, j^ = m^ where m is the remainder of ij on division by. 7
(thus , 5^°3^ = 1^ since..5.3 =15 has 1 as remainder on the division by 7)
Prove that R is a commutative ring with unit element.

The complete problem is in the attached file.

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Solution Summary

The Solution proves that R, the set of integers mod 7 under the addition and multiplication mod 7 is a commutative ring with unit element.

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  • BSc, Manipur University
  • MSc, Kanpur University
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