-essential subgroups of abelian groups. I
For an arbitrary infinite cardinal , we define classes of -cslender and -tslender modules as well as related classes of -hmodules and initiate a study of these classes.
For many domains R (including all Dedekind domains of characteristic 0 that are not fields or complete discrete valuation domains) we construct arbitrarily large superdecomposable R-algebras A that are at the same time E(R)-algebras. Here "superdecomposable" means that A admits no (directly) indecomposable R-algebra summands ≠ 0 and "E(R)-algebra" refers to the property that every R-endomorphism of the R-module, A is multiplication by an element of, A.