Atoms in infinite dimensional free sequence-set algebras
ALGEBRA UNIVERSALIS, cilt.80, sa.4, 2019 (SCI-Expanded, Scopus)
- Yayın Türü: Makale / Tam Makale
- Cilt numarası: 80 Sayı: 4
- Basım Tarihi: 2019
- Doi Numarası: 10.1007/s00012-019-0610-8
- Dergi Adı: ALGEBRA UNIVERSALIS
- Derginin Tarandığı İndeksler: Science Citation Index Expanded (SCI-EXPANDED), Scopus
- Anahtar Kelimeler: Free algebras, Cylindric-like algebras, Atoms and zero-dimensional elements
- İstanbul Medipol Üniversitesi Adresli: Hayır
Özet
A. Tarski proved that the m-generated free algebra of CA α, the class of cylindric algebras of dimension α, contains exactly 2 m zero-dimensional atoms, when m≥ 1 is a finite cardinal and α is an arbitrary ordinal. He conjectured that, when α is infinite, there are no more atoms other than the zero-dimensional atoms. This conjecture has not been confirmed or denied yet. In this article, we show that Tarski’s conjecture is true if CA α is replaced by D α, G α, but the m-generated free Crs α algebra is atomless.