Almost-free -algebras and E(A,R)-modules
Volume 169 / 2001
Fundamenta Mathematicae 169 (2001), 175-192
MSC: 20K20, 20K30, 16W20.
DOI: 10.4064/fm169-2-6
Abstract
Let R be a unital commutative ring and A a unital R-algebra. We introduce the category of E(A,R)-modules which is a natural extension of the category of E-modules. The properties of E(A,R)-modules are studied; in particular we consider the subclass of E(R)-algebras. This subclass is of special interest since it coincides with the class of E-rings in the case R={\mathbb Z}. Assuming diamond \diamond , almost-free E(R)-algebras of cardinality \kappa are constructed for any regular non-weakly compact cardinal \kappa > \aleph _0 and suitable R. The set-theoretic hypothesis can be weakened.
