It is proved that every distributive algebraic lattice such that its compact elements form a lattice with unit can be represented as the congruence lattice of some semigroup without idempotents. This implies that every distributive algebraic lattice with at most countably many compact elements is also representable as the congruence lattice of a semigroup without idempotents.
|Translated title of the contribution||Representation of lattices by congruence lattices of semigroups without idempotents|
|Number of pages||10|
|Journal||Труды института математики и механики УрО РАН|
|Publication status||Published - 2012|
Level of Research Output
- VAK List