Subtractive nearsemilattices. (English) Zbl 1027.06007

Cīrulis, Jānis

Proc. Latv. Acad. Sci., Sect. B, Nat. Exact Appl. Sci. 52, No. 5, 228-233 (1998).

Summary: The standard definition of a subtraction in a join semilattice is adapted for nearsemilattices, i.e. posets in which any finite subset possessing an upper bound has a unique least upper bound. The elementary arithmetic in such partial semilattices is developed to show that most properties of subtraction extend to this case. However, the problem of whether the operation is unique in any nearsemilattice remains open.

MSC:

06A12	Semilattices
08A55	Partial algebras

Keywords:

Henkin algebra; partial join; relative subalgebra; subtractive semilattice; subtraction; nearsemilattices; partial semilattices