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An observation on Krull and derived dimensions of some topological lattices

M. Rostami; Ilda I. Rodrigues — 2011

Archivum Mathematicum

Let $(L, \leq)$ , be an algebraic lattice. It is well-known that $(L, \leq)$ with its topological structure is topologically scattered if and only if $(L, \leq)$ 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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