  In this paper we develop a general theory of modules which are invariant
under automorphisms of their covers and envelopes. When applied to specific
cases like injective envelopes, pure-injective envelopes, cotorsion envelopes,
projective covers, or flat covers, these results extend and provide a much more
succinct and clear proofs for various results existing in the literature. Our
results are based on several key observations on the additive unit structure of
von Neumann regular rings.
