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An observation on Krull and derived dimensions of some topological lattices

M. Rostami;  Ilda I. Rodrigues — 2011

Archivum Mathematicum

Let ( L , ≤ ) , be an algebraic lattice. It is well-known that ( L , ≤ ) with its topological structure is topologically scattered if and only if ( L , ≤ ) 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 error L , the set of all prime elements of L . Hence the dimensions on the lattice...

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