ACTA MATHEMATICA UNIVERSITATIS COMENIANAE

Vol. 60,   1   (1991)
pp.   153-156

ON DIRECT DECOMPOSITIONS OF CERTAIN ORTHOMODULAR LATTICES
P. KON\OPKA and S. PULMANNOVA

Abstract.  Let $L$ be an orthomodular lattice. For $a,b\in L$ define $a\pl^cb$ if either $a$ and $b$ both belong to the centre $C(L)$ of $L$ or if $\a,b\\cap C(L)=\emptyset$ and $a\pl b$ (i.e. $a$ is compatible with $b$). Let $R$ be the transitive closure of the relation $\pl^c$. Then there exist at least three equivalence classes of the relation $R$ in $L$ if and only if either $L$ is a horizontal sum (if $C(L)=\0,1\$) or $L$ is a direct product of a Boolean algebra and a horizontal sum.

AMS subject classification.  06B05, 81B10
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