Almost-free E(R)-algebras and E(A,R)-modules

• Autorzy: Rüdiger Göbel , Lutz Strüngmann
• Języki publikacji: EN

Abstrakty

EN

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 = ℤ. Assuming diamond ⋄, almost-free E(R)-algebras of cardinality κ are constructed for any regular non-weakly compact cardinal κ > ℵ ₀ and suitable R. The set-theoretic hypothesis can be weakened.

Kategorie tematyczne

• 16W20: Automorphisms and endomorphisms
• 20K30: Automorphisms, homomorphisms, endomorphisms, etc.
• 20K20: Torsion-free groups, infinite rank

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Fundamenta Mathematicae
• Rocznik: 2001
• Tom: 169
• Numer: 2
• Strony: 175-192

Daty

wydano

2001

Twórcy

autor

Rüdiger Göbel

• Fachbereich 6, Mathematik und Informatik, Universität Essen, 45117 Essen, Germany

autor

Lutz Strüngmann

• Fachbereich 6, Mathematik und Informatik, Universität Essen, 45117 Essen, Germany

Identyfikatory

DOI

10.4064/fm169-2-6