We prove that there exist finitely generated algebras, which are pseudosimple but not simple. This problem goes back to Henkin, Monk, Tarski . In fact, for any limit ordinal i, there exists a pseudosimple algebra, which has no proper subalgebra and whose congruence lattice is ωi+1. (Here ωi denotes ordinal power).
ASJC Scopus subject areas
- Algebra and Number Theory