CHARACTERIZATION OF AUTOMORPHISM-INVARIANT MODULE BY ITS INJECTIVITY

• Main Author: Syafrian Putri, Inne
• Format: Theses
• Language: Indonesia
• Subjects: Matematika
• Online Access: https://digilib.itb.ac.id/gdl/view/34872
• Institution: Institut Teknologi Bandung

Let M be a module over ring R. An Injective hull of M, denoted by E(M), is an injective module which contain M as its essential submodule. If M is invariant under any automorphism of E(M), then M is called an automorphism- invariant module. Direct summand of an automorphism-invariant module is automorphism-invariant, and if the direct sum M1 o M2 is automorphism-invariant then M1 dan M2 are relatively injective. The sufficient and neces- sary condition for a module M to be automorphism-invariant is every isomor-phism between two essential submodules of M extend to an endomorphism of M. This gives a result that every pseudo-injective module is automorphism-invariant. In this thesis showed that the module M is automorphism-invariant if and only if M pseudo-injective.