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A continuous lattice L with DID(L) incomplete.

R.E. Hoffmann (1986)

Semigroup forum

A maximal chain approach to topology and order.

Vainio, R. (1988)

International Journal of Mathematics and Mathematical Sciences

A note on topology of $Z$ -continuous posets

Venu G. Menon (1996)

Commentationes Mathematicae Universitatis Carolinae

$Z$ -continuous posets are common generalizations of continuous posets, completely distributive lattices, and unique factorization posets. Though the algebraic properties of $Z$ -continuous posets had been studied by several authors, the topological properties are rather unknown. In this short note an intrinsic topology on a $Z$ -continuous poset is defined and its properties are explored.

A partically ordered space which is not a Priestely space.

A. Stralka (1980)

Semigroup forum

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...