An extension of relative pseudocomplementation to non-distributive lattices. (English) Zbl 1048.06005

Chajda, Ivan

Acta Sci. Math. 69, No. 3-4, 491-496 (2003).

Summary: We characterize lattices \(L\) with 1 where for each element \(p\) the interval \([p,1]\) is a pseudocomplemented lattice. Moreover, if for \(x,y\in L\) the relative pseudocomplement \(x*y\) exists then it is equal to the pseudocomplement of \(x\lor y\) in \([y,1]\). However, the latter exists for each \(x\), \(y\) also, e.g., in \(N_5\), contrary to the case of relatively pseudocomplemented lattices which are distributive.

MSC:

06D15

Pseudocomplemented lattices

Keywords:

nondistributive lattices; pseudocomplemented lattice