ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 6,20 Tokizawa, Masamichi, Chuo University, Japan Set product residue semigroups. An equivalence relation ρ_{H} on a semigroup S is defined by aρ_{H}b ⟺ aH = bH(a, b ∈ S) where H ⊂ S. If, for any pair a, b ∈ S, there exists c ∈ S such that (aH)(bH) = cH (called set product condition), then we can define an associative multiplication ā ∗ b̄ = c̄ in S/ρ_{H}. We call (S/ρ_{H}, ∗) the set product residue semigroup of S with respect to H. In general, ā ∗ b̄ ≠ \overline{ab}. A homomorphism theorem and examples including a semigroup in which, every subset satisfies the set product condition, will be presented. A lattice theoretic aspect of the idempotent semigroup is related to this notion.