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A characterization of algebras of invariant-coinvariant module type


Author: Ryohei Makino
Journal: Proc. Amer. Math. Soc. 92 (1984), 10-12
MSC: Primary 16A48; Secondary 16A64
DOI: https://doi.org/10.1090/S0002-9939-1984-0749880-1
MathSciNet review: 749880
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Abstract: K. R. Fuller has characterized rings of left invariant module type. An algebra is said to be of invariant-coinvariant module type if each of its indecomposable modules is quasi-injective or quasi-projective. In this note we shall give a characterization of algebras of invariant-coinvariant module type, which distinguishes this class from that of algebras of local-colocal type. It seems of interest that the distributivity of second radicals of primitive ideals appears in our characterization.


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Additional Information

DOI: https://doi.org/10.1090/S0002-9939-1984-0749880-1
Keywords: Algebra of local-colocal type, distributive module, quasi-injective module, quasi-projective module
Article copyright: © Copyright 1984 American Mathematical Society

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