Abstract
In the early 1990s, Harada and Oshiro introduced extending and lifting properties for modules and, simultaneously, considered two new classes of artinian rings which contain quasi-Frobenius (QF-) rings and Nakayama rings: one is the class of right Harada rings and the other is the class of right co-Harada rings. Although QF-rings and Nakayama rings are left-right symmetric, Harada and co-Harada rings are not left-right symmetric. However, Oshiro showed that left Harada rings and right co-Harada rings are coinside. In this paper we provide many characterizations of right co-Harada rings and (right and left) co-Harada rings.
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