### A topology with order, graph and an enumeration problem.

Skip to main content (access key 's'),
Skip to navigation (access key 'n'),
Accessibility information (access key '0')

Back to Simple Search
# Advanced Search

Let $(L,\le )$, be an algebraic lattice. It is well-known that $(L,\le )$ with its topological structure is topologically scattered if and only if $(L,\le )$ is ordered scattered with respect to its algebraic structure. In this note we prove that, if $L$ is a distributive algebraic lattice in which every element is the infimum of finitely many primes, then $L$ has Krull-dimension if and only if $L$ has derived dimension. We also prove the same result for $errorL$, the set of all prime elements of $L$. Hence the dimensions on the lattice...

**Page 1**