# Abstract algebra: define constants in a finite field

How can I to define a constant in $Z_{2}$?

For example, I want to create a constant b that inherits the properties of an element from $Z_{2}$. For example

b + b = 0
b^n = b

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Your question focuses on the wrong aspect of finite fields. It's not the numbers 0 and 1 that change because you are working with $Z_2$, it's the arithmetic operators. You could define your own operators plusZ2 and TimesZ2.
An alternative is to load the finite fields package with Needs[FiniteFields], which overloads the relevant arithmetic operators for you.
Great! You are right! Thanks. But... I have some large polynomials whose coefficients are in $Z_{2}$... for example: $p(X)=(a+b^2+c^4+5b^6....)X+(.....)X^2+....$ So, how can I simplify $(a+b^2+c^4+5b^6....)$ in a authomatic way? (suppose $(a+b^2+c^4+5b^6...)$ is in arithmetic of $Z_2$) –  user14545 May 22 at 20:53