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Characterizations of right Nakayama rings

Published online by Cambridge University Press:  18 May 2009

Manabu Harada
Manabu Harada
Affiliation:
Department of Mathematics, Osaka City University, Sugimoto-3, Sumiyosi-Ku, Osaka 558, Japan
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We have studied relationships between almost relative projectivity and Nakayamaings [8]. In this paper we shall further investigate certain characterizations of right Nakayama rings in terms of almost relative projectives (or injectives). We shall consider three conditions (A), (B) and (C) (see Section 1), which are always satisfied for the relative projective modules, but not for almost relative projectives in general. As an application of [9, Theorem] and [10, Theorem 2], we shall show that a right artinian ring is right Nakayama if and only if one of the above three conditions holds true for almost relative projectives (Corollary to Theorem 1). Moreover we shall give a characterization of two-sided Nakayama rings related to (C) and the dual (C#) (Theorem 2). Finally we shall investigate the transitivity of almost relative projectives, which is the converse of (B), and give some characterizations of right Nakayama rings related to the transitivity.

Type
Research Article
Information
Glasgow Mathematical Journal , Volume 34 , Issue 1 , January 1992 , pp. 91 - 102
Copyright
Copyright © Glasgow Mathematical Journal Trust 1992

References

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