Abstract. In this paper different constrained abstract representation theorems for partial groupoids and semigroups are proved. Methods for improving the retract properties of the structures are also developed. These have strong class-theoretical implications for many types of generalized periodic semigroups and related partial semigroups. The results are significant in a model-theoretical setting.
2000 Mathematics Subject Classification. 20M10, 08A55.
Key words and phrases. Constrained abstract representation problems, retracts, retract extensions, partial semigroups, partial groupoids, generalized periodic semigroups, CSM-types.