Modules invariant under monomorphisms of their envelopes

Guil Asensio P. A. , KESKİN TÜTÜNCÜ D. , Srivastava A. K.

ADVANCES IN RINGS AND MODULES, cilt.715, ss.171-179, 2018 (SCI İndekslerine Giren Dergi) identifier

  • Cilt numarası: 715
  • Basım Tarihi: 2018
  • Doi Numarası: 10.1090/conm/715/14410
  • Sayfa Sayıları: ss.171-179


In this paper we prove that a module M is invariant under automorphisms of its X-envelope if and only if M is invariant under monomorphisms of its X-envelope where X is an enveloping class with the property that for each object X in X, End(X)/J(End(X)) is a von Neumann regular right self-injective ring and idempotents lift modulo J(End(X)). In particular, invariance under monomorphisms is equivalent to the invariance under automorphisms of X-envelope when X is the class of injective modules, pure-injective modules or flat cotorsion modules. We finish the paper by proving that an X-automorphism invariant (equivalently, X-monomorphism invariant) module M satisfies the property P if and only if its X-envelope X(M) satisfies the property P, when P is direct-finiteness, internal cancellation, cancellation or the substitution property.