Commutative perfect 𝑄𝐹-1 rings

Tachikawa, Hiroyuki

doi:10.1090/S0002-9939-1978-0472903-1

Commutative perfect $\textrm {QF}-1$ rings
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Proc. Amer. Math. Soc. 68 (1978), 261-264 Request permission

Abstract:

If R is a commutative artinian ring, then it is known that every finitely generated faithful R-module is balanced (i.e. has the double centralizer property) if and only if R is a quasi-Frobenius ring. In this note, constructing new nonbalanced modules we prove that the assumption on R to be artinian can be replaced by the weaker condition that R is perfect.

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A property of QF-1 rings

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