Abstract. The aim of the present paper is to generalize a result of Gábor Czédli. We estimate the maximum of the number of brick islands of ${\bf m_1\times m_2\times\cdots \times m_d}$, for any $d\geq3$ and for any fixed $d$-tuple $(m_1,m_2,\ldots,m_d)$ of positive integers.

AMS Subject Classification (1991): 05A16, 06D99

Keyword(s): lattice, distributive lattice, weakly independent subset, weak basis, brick island, number of islands

Received February 11, 2008, and in revised form February 18, 2008. (Registered under 6056/2009.)