A characterization of algebras of invariant-coinvariant module type

Makino, Ryohei

doi:10.1090/S0002-9939-1984-0749880-1

A characterization of algebras of invariant-coinvariant module type
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Proc. Amer. Math. Soc. 92 (1984), 10-12 Request permission

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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