Skew nearlattices: some structure and representation theorems. (English) Zbl 1234.06004

Cīrulis, Jānis

Chajda, I. (ed.) et al., Proceedings of the 79th workshop on general algebra “79. Arbeitstagung Allgemeine Algebra”, 25th conference of young algebraists, Palacký University Olomouc, Olomouc, Czech Republic, February 12–14, 2010. Klagenfurt: Verlag Johannes Heyn (ISBN 978-3-7084-0407-3/pbk). Contributions to General Algebra 19, 33-44 (2010).

A nearlattice is a meet semilattice in which every principal order ideal is a lattice. A skew nearlattice is a nearlattice with non-commutative meet operation. Such a nearlattice is called right normal (an rns-nearlattice, for short) if a weakened commutative law \(xyz=yxz\) holds. In this paper the structure of rns-nearlattices is characterized. Several representation theorems for these algebras are also given.
For the entire collection see [Zbl 1201.08001].

Reviewer: Marius Tărnăuceanu (Iaşi)

MSC:

06A12	Semilattices
08A55	Partial algebras
20M10	General structure theory for semigroups

Keywords:

right normal band; function algebra; scheme homomorphism; skew nearlattice