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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
Keyword(s):
lattices,
absorption laws,
associativities,
distributivities
Received February 3, 2005, and in final form June 8, 2006. (Registered under 5933/2009.)
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