| Version 3 |
Version 2 |
| Let $A$ be a relation algebra with operators $(\vee,\wedge,\ ;,',^-,0,1,i)$ of type $(2,2,2,1,1,0,0,0)$. Then $a\in A$ is called a |
Let $A$ be a relation algebra with operators $(\vee,\wedge,\ ;,',^-,0,1,i)$ of type $(2,2,2,1,1,0,0,0)$. Then $a\in A$ is called a |
| \begin{itemize} |
\begin{itemize} |
| \item \emph{function element} if $e^-\ ; e\le i$, |
\item \emph{function element} if $e^-\ ; e\le i$, |
| \item \emph{injective element} if it is a function element such that $e\ ; e^-\le i$, |
\item \emph{injective element} if it is a function element such that $e\ ; e^-\le i$, |
|
\item \emph{surjective element} if $e^-\ ;e=i$,
|
\item \emph{surjective element} if it is a function element such that $i\le e^-\ ;e$,
|
| \item \emph{reflexive element} if $i\le a$, |
\item \emph{reflexive element} if $i\le a$, |
| \item \emph{symmetric element} if $a^-\le a$, |
\item \emph{symmetric element} if $a^-\le a$, |
| \item \emph{transitive element} if $a\ ; a\le a$, |
\item \emph{transitive element} if $a\ ; a\le a$, |
| \item \emph{subidentity} if $a\le i$, |
\item \emph{subidentity} if $a\le i$, |
| \item \emph{antisymmetric element} if $a\wedge a^-$ is a subidentity, |
\item \emph{antisymmetric element} if $a\wedge a^-$ is a subidentity, |
| \item \emph{equivalence element} if it is symmetric and transitive (not necessarily reflexive!), |
\item \emph{equivalence element} if it is symmetric and transitive (not necessarily reflexive!), |
| \item \emph{domain element} if $a\ ; 1 = a$, |
\item \emph{domain element} if $a\ ; 1 = a$, |
| \item \emph{range element} if $1\ ; a=a$, |
\item \emph{range element} if $1\ ; a=a$, |
| \item \emph{ideal element} if $1\ ; a\ ; 1=a$, |
\item \emph{ideal element} if $1\ ; a\ ; 1=a$, |
| \item \emph{rectangle} if $a=b\ ; 1\ ; c$ for some $b,c\in A$, and |
\item \emph{rectangle} if $a=b\ ; 1\ ; c$ for some $b,c\in A$, and |
| \item \emph{square} if it is a rectangle where $b=c$ (using the notations above). |
\item \emph{square} if it is a rectangle where $b=c$ (using the notations above). |
| \end{itemize} |
\end{itemize} |
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| More to come... |
More to come... |
