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Sunday, October 4, 2015

UTM Ideals Varieties and Algorithm - Chapter 1 Section 1 Exercise 1

Problem:



Solution:

Instead of exhausting the formula, it is easier to describe and prove by defining those operation as mod 2 operations.

Now addition mod 2 is closed, associative, commutative, has identity 0 and inverse well defined.

Multiplication is closed, associative, commutative and distributive under addition.
The only non trivial thing is multiplicative inverse, but that is trivial for mod 2 because the only element need a multiplicative is 1, which is simply itself.

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