@PedroTamaroff An outline of a nice way to prove that the complement of a saturated multiplicative set is a union of prime ideals is as follows:
(1) Given a multiplicative set $S$, define it's saturation $\hat S=\{x\in A: \exists y, xy\in S\}$. Show that $\hat S$ is saturated.
(2) Saturations relate to localization as follows; if $S^{-1}A=T^{-1}A$, then $T\subseteq\hat S$.
(3) The prime ideals of a localization $S^{-1}A$ are of the form $\mathfrak pS^{-1}A$ where $\mathfrak p$ is disjoint from $S$.
Like we know, the standard form of KdV equation is
(1) $u_{t}-6uu_{x}+u_{xxx}=0$,
where this equation describes a solitary wave propagation and $u=u(x,t)$.
On the other hand, we know the classical wave equation
(2) $\frac{{\partial}^{2}u}{{\partial}t^{2}}-\frac{{\partial}^{2}u}{{\parti...
Question : A Partial Injective Relation from $A \rightarrow B$ is maximal if its graph of an injection function from $A$ to $B$ or the graph of an injection function from $B$ to $A$.
Example: $A =[a,b,c]$ and $B=[1,2,3,4]$.
Build a partial injection relation. Are there 3-4 elements or a lot o...
