ICM 1998, Berlin, Aug. 18–27

Abstracts of Short Communications and Posters

Section:

2. Algebra

1991 MS Classification: 06, 08, 20, 68 Miroslav D. Ćirić, University of Niš, Yugoslavia Atomic decompositions of algebras and structures A type Δ of decompositions of algebras or structures of type τ is called atomic if every algebra or structure of type τ has a Δ-decomposition whose components are Δ-indecomposable. The most known atomic type are subdirect decompositions. However, atomic decompositions are not numerous. For example, except the subdirect products, only four atomic decompositions of semigroups are known. We shall present various atomic decompositions of semigroups, automata, ordered sets etc. These results are joint work with Stojan Bogdanović.