ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 6, 8 Horiuchi, Kiyomitsu, Konan University, Japan An expansion of lattice A lattice L have two operations, ∨ (join) and ∧ (meet). (L, ∨) and (L, ∧) are semilattices, respectively. Then, there are two order relations, a ≤_{∨} b ⇔ a ∨ b = b and a ≤_{∧} b ⇔ a ∧ b = b. From the absorption law, the order ≤_{∨} is quite reverse order of the order ≤_{∧}. Lattice can be considered an expression to the one dimensional reversible situation. A new three semilattices system with roundabout-absorption law will be presented. The roundabout-absorption law on it is analogous to absorption law on lattice.