In this paper, we study the conditions under which an automorphism of a dense subring of
the endomorphism ring of a free module is induced by a semilinear isomorphism of the …

Abstract Motivated by [1], we study on\tau-lifting modules (rings) and\tau-semiperfect
modules (rings) for a preradical\tau and give some equivalent conditions. We prove that; i) if …

An R-module F is called closed (neat) projective if, for every closed (neat) submodule L of
every R-module M, every homomorphism from F to M/L lifts to M. In this paper, we study …

In this paper, we give some results of indecomposable rings in which finitely generated right
ideals are automorphism-invariant. They are called fa-rings. It shows that any …

The paper contains both known and new results on automorphism-invariant modules,
automorphism-coinvariant modules and modules which are invariant or coinvariant with …

It is proved, among other results, that a prime right nonsingular ring (in particular, a simple
ring) R is right self-injective if RR is invariant under automorphisms of its injective hull. This …

It is shown that if R is a right automorphism-invariant ring and satisfies ACC on right
annihilators, then R is a semiprimary ring. By this useful fact, we study finiteness conditions …

Automorphism-liftable modules Page 1 May 19, 2022 13:6 WSPC/S0219-4988 171-JAA
2250106 Journal of Algebra and Its Applications Vol. 21, No. 6 (2022) 2250106 (11 pages) c© …

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 …

A module M is called N-almost-invariant for a module N if, for any homomorphism α: F→ E,
either α (N)⊆ M, or there exist nonzero direct summands F′ of F and E′ of E such that α …