Abstract. 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 $x\ast y$ exists then it is equal to the pseudocomplement of $x\vee y$ 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, see e.g. [1], [2], [3].

AMS Subject Classification (1991): 06D15, 06D20

Keyword(s): Relative pseudocomplement, pseudocomplement, semidistributive lattice

Received March 11, 2002, and in revised form May 9, 2002. (Registered under 2911/2009.)