Superdecomposable E(R)-Algebras

ABSTRACT

An E-ring is a ring that is naturally isomorphic to the endomorphism ring of its additive group. E-rings with various properties have been constructed in the literature; we now consider superdecomposable E-rings. More generally, we construct superdecomposable algebras A over integral domains R, which are at the same time E(R)-algebra in the sense that the ring of R-endomorphisms of the underlying R-module structure is canonically isomorphic to A. We also establish the existence of arbitrarily large superdecomposable modules over such algebras.

Key Words:

• E-algebra
• E(R)-algebra
• Module
• Superdecomposable

1991 Mathematics Subject Classification:

• Primary 13C13
• Secondary 13F99
• 20K20

ACKNOWLEDGMENT

The authors thank the referee for several useful comments.

Notes

^# Communicated by K. Rangaswamy.