A module is called automorphism-invariant if it is invariant under any
automorphism of its injective hull. In [Algebras for which every indecomposable
right module is invariant in its injective envelope, Pacific J. Math., vol. 31,
no. 3 (1969), 655-658] Dickson and Fuller had shown that if R is a
finite-dimensional algebra over a field F with more than two elements
then an indecomposable automorphism-invariant right R-module must be
quasi-injective. In this paper we show that this result fails to hold if
F is a field with two elements. Dickson and Fuller had further shown
that if R is a finite-dimensional algebra over a field F with more
than two elements, then R is of right invariant module type if and only if
every indecomposable right R-module is automorphism-invariant. We extend the
result of Dickson and Fuller to any right artinian ring. A ring R is said to
be of right automorphism-invariant type (in short, RAI-type) if every finitely
generated indecomposable right R-module is automorphism-invariant. In this
paper we completely characterize an indecomposable right artinian ring of
RAI-type.Comment: To appear in Contemporary Mathematics, Amer. Math. So