Abstract. This article defines cancellative coextensions and generalized coset extensions for commutative semigroups and studies their first properties, including their relationship to Ponizovsky families and completions.

AMS Subject Classification (1991): 20M14

Keyword(s): cancellative coextension, generalized coset, congruence, commutative semigroup, subelementary semigroup, subcomplete semigroup, Ponizovsky family, completion

Received August 14, 2002. (Registered under 2916/2009.)