Relatively morphic submodules are defined and a new class of modules between morphic and Hopfian modules is singled out. Special care is given to the Abelian groups case.

It is proved that the commutator subgroup of the fundamental group of the complement of any plane affine irreducible Hurwitz curve (respectively, any plane affine irreducible pseudoholomorphic curve) is finitely presented. It is shown that there exists a pseudo-holomorphic curve (a Hurwitz curve) in CP whose fundamental group of the complement is not Hopfian and, respectively, this group is not...

Abstract We introduce a notion of topologically flat locally convex module, which extends the Banach module and is well adapted to nonmetrizable setting (and especially DF-modules). Using this notion, we amenable algebras show that complete barrelled DF-algebra if only it Johnson amenable, extending thereby Helemskii–Sheinberg’s criterion for algebras. As an application, completely characterize...

In this paper we introduce R-right (left), L-left (right) cancellative and weakly R(L)-cancellative semigroups and will give some equivalent conditions for completely simple semigroups, (completely) regular right (left) cancellative semigroups, right (left) groups, rectangular groups, rectangular bands, groups and right (left) zero semigroups according to R-right (left), L-left (right) and weak...