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- W1646891135 abstract "SURJEET SINGH AND ASHISH K. SRIVASTAVADedicated to T. Y. Lam on his 70 th BirthdayAbstract. A module is called automorphism-invariant if it is invariant underany automorphism of its injective hull. In [Algebras for which every indecom-posable right module is invariant in its injective envelope, Pacific J. Math.,vol. 31, no. 3 (1969), 655-658] Dickson and Fuller had shown that if R isa finite-dimensional algebra over a field F with more than two elements thenan indecomposable automorphism-invariant right R-module must be quasi-injective. In this paper we show that this result fails to hold if F is a fieldwith two elements. Dickson and Fuller had further shown that if Ris a finite-dimensional algebra over a field Fwith more than two elements, then R is ofright invariant module type if and only if every indecomposable right R-moduleis automorphism-invariant. We extend the result of Dickson and Fuller to anyright artinian ring. A ring R is said to be of right automorphism-invarianttype (in short, RAI-type) if every finitely generated indecomposable right R-module is automorphism-invariant. In this paper we completely characterizean indecomposable right artinian ring of RAI-type." @default.
- W1646891135 created "2016-06-24" @default.
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- W1646891135 date "2014-01-01" @default.
- W1646891135 modified "2023-10-18" @default.
- W1646891135 title "Rings of Invariant Module Type and Automorphism-Invariant Modules" @default.
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- W1646891135 doi "https://doi.org/10.1090/conm/609/12090" @default.
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