Abstract. It is well-known that for lattices both associativities are equivalent to the transitivity of the corresponding partially ordered set. It is also well-known that both distributivity is equivalent to the medial identity. We shall prove that ``in general'' this is not the case. Some related topics will be investigated.
AMS Subject Classification
(1991): 08B99, 08B10, 06D99
Received February 3, 2005, and in final form June 8, 2006. (Registered under 5933/2009.)