User:Ppol10/sandbox

2nd Definition
An ideal lattice is a lattice ${\textit {(I,b)}}$, where ${\textit {I}}$ is a (fractional) ${\textit {O}}$-ideal and ${\textit {b}}:{\textit {I}}\times {\textit {I}}\longrightarrow {\textbf {R}}$ is such that

$b(\lambda x,y)=b(x,{\overline {\lambda }}y)$

for all $x,y\in {\textit {I}}$ and for all $\lambda \in {\textit {O}}$.


As a $\mathbb {Z}$-module, $\mathbb {Z} [x]/\langle f\rangle$ is isomorphic to $\mathbb {Z} ^{n}$ regardless of the choice of $f$.

For simplicity, some studies only concentrate on rings of the form $\mathbb {Z} [x]/\langle x^{n}+1\rangle$, as they have proved to be the most useful for practical applications .


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