On Countable Completions of Quotient Ordered Semigroups

Samy Abbes (1)

1 PPS - Preuves, Programmes et Systèmes

We study the commutativity of two operations: quotienting and completing. Completing refers to the countable chain completion, known to exist in every partial order, and quotienting is with respect to a semigroup congruence. The two operations are shown to commute in a suitable framework. We apply the results for studying the semigroup structure and topological semigroup structure on the completion.

Keywords: Completion; ordered semigroup

Domains: Other [cs.OH]

Samy Abbes. On Countable Completions of Quotient Ordered Semigroups. Semigroup Forum, 2008, 77 (3), pp.482-499. ⟨10.1007/s00233-008-9111-3⟩. ⟨hal-00349207⟩