Strongly simply connected algebras (Q1270041)

The authors present characterizations and construction techniques for strongly simply connected algebras. First, they give an alternative definition for strongly simply connectedness for locally bounded categories and then obtain a handy criterion to verify whether a locally bounded category is strongly simply connected. In particular, Schurian strongly simply connected locally bounded categories are further studied. As to the question how to construct strongly simply connected algebras, the authors show that an algebra is strongly simply connected if and only if it is the one-point extension (or coextension) of a strongly simply connected algebra by a completely coseparated module (or a completely separated module, respectively).