A module is called generalized Hopfian (gH) if any of its surjective endomorphisms has a
small kernel. Such modules are in a sense dual to weakly co-Hopfian modules that were …

Let R be a ring and M a left R‐module. M which satisfies DCC on essential submodules is
GCH, and M which satisfies ACC on small submodules is WH. If M [X] is GCH R [X]‐module …

An R-module M is called strongly Hopfian (respectively strongly co-Hopfian) if for every
endomorphism f of M the chain Kerf⊆ Kerf2⊆⋯(respectively Imf⊇ Imf2⊇⋯) stabilizes. The …

In this paper we introduce the notion of μ μ-Hopfian modules which is a proper
generalization of that of Hopfian modules. We give some characterizations and properties of …

Ar-module M is said to be Hopfian (respectively Co-Hopfian) in case any surjective
(respectively injective) R-homomorphism is automatically an isomorphism. In this paper we …

MODULES WITH DEDEKIND FINITE ENDOMORPHISM RINGS A unital ring R is called
Dedekind (or directly, or von Neumann) finite if ba = Page 1 MATHEMATICA, Tome ?? (??), No …

Hopfian modules and co-hopfian modules Page 1 COMMUNICATIONS IN ALGEBRA, 23(4),
1219-1229 (1995) HOPFIAN MODULES AND GO-HOPFIAN MODULES Weimin Xue …

An R-module M is called weakly co-Hopfian if any injective endomorphism of M is essential.
The class of weakly co-Hopfian modules lies properly between the class of co-Hopfian and …

A left R-module M is said to be Hopfian if any surjective R-homomorphism is automatically
an isomophism. It is well-known that any left noetherian R-module is Hopfian. In [5], it was …

Alt the rings we consider will be associative with 1~ 0; all the ring homomorphisms will be
required to preserve the identity elements. All the modules we consider will be unitary …