Q: Ideal generated by a set of polynomials $X^{a/b}$ where each monomial having $a$ and not having $b$ Let 
$$\mathcal R=\mathbb Z_2[x_1,\dots,x_n]/\langle x_1^2-x_1,\dots,x_n^2-x_n\rangle.$$ 
I want to learn ideal arithmetics to deal with polynomials of the forms such as


*

*Consider a set of polynomials 
$$X^{a/b}=\{ x^\gamma \mid a\in \gamma, b\not\in\gamma,\gamma\in\mathcal R \}$$ 
where $x^\gamma$ is a monomial like $x_1x_2x_5x_a$ such that each monomial has an indeterminate $a$ and each monomial does not have an indeterminate $b$. Consider the ideal $I^{a/b}$ that is a set of polynomials where each monomial has an indeterminate $a$ and each monomial does not have an indeterminate $b.$ 

*Now consider 
$$X^{A\backslash B}=\{ x^\gamma \mid \gamma\in A, \gamma\not\in B,\gamma\in\mathcal R\}$$
where $A$ and $B$ are subsets of $\{1,2,\ldots,n\}$ that is $X^{A\backslash B}$ is a set of all monomials that contains $x_i$ with $i\in A$ and $x_j$ with $j\not\in B$. Then $X^{A\backslash B}$ in fact generates the ideal $I^{A\backslash B}$.


So
Where can you find books and references on ideal arithmetics dealing with polynomials having the ground ring $\mathcal R$?
