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Let R = {0, 2, 4, 6, 8} under addition and multiplication modulo 10. Prove that...

Let R = {0, 2, 4, 6, 8} under addition and multiplication modulo 10. Prove that R is
a field.

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Answer #1

Solution:

  is a commutative ring

Consider the multiplication table

Since

   is the multiplicative identity

Also,

Thus every element of   has multiplicative inverse

  is a field.

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