Abstract
Fuller [Fuller, K. R. (1969). On indecomposable injectives over artinian rings. Pacific J. Math. 29:115–135] has proved that a right artinian ring is a right Nakayama and right co-Nakayama ring if and only if it is a two-sided Nakayama artinian ring. Oshiro [Oshiro, K. (1989). On Harada rings I. Math. J. Okayama Univ. 31:161–178] has proved that a right artinian ring is a right Nakayama QF-3 ring if and only if it is a two-sided Nakayama artinian ring. These results poses a question whether a right co-Nakayama ring and right QF-3 ring is two-sided Nakayama artinian. First Theorem 1.4 proves this question affirmatively. Next using this result and properties of one-sided Harada rings, we shall give some characterizations of Nakayama rings.
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