In [10, Theorem 3.1] K. R. Fuller characterized indecomposable injective pro-jective modules over artinian rings using i-pairs. In [3] the author generalizedthis theorem to indecomposable projective quasi-injective modules and inde-composable quasi-projective injective modules over artiniain rings. In [2] theauthor and K. Oshiro studied the above Fuller's theorem minutely. And M.Morimoto and T. Sumioka generzlized these results to modules in [17]. Furtherin [13] M. Hoshino and T. Sumioka extended the results in [3] to perfect ringsand consider the condition "colocal pairs". Furthermore in [7] the auther stud-ied the results in [3] from the point of view of [2] and [13] and gave resultson colocal pairs. The purpose of this note is to report about this development.
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机译：在[10，定理3.1] K. R.Fumer使用i-彼此的在Artinian环上表征了不可分解的重新注射的卓越型模块。在[3]中，作者通过Artiniain环上的不可分解的投影准重新注射模块和Inde-Composable准投射模块的定理。在[2] Theauthor和K. Oshiro仔细研究了上述富勒的定理。和m.morimoto和t. sumioka在[17]中的模块中流动了这些结果。进一步[13] M. Hoshino和T. Sumioka将结果延长至完美的戒指和考虑条件“结源对”。此外，在[7]中，从[2]和[13]的角度来看，在[3]中的结果中的结果，并给出了结果结合对。本说明的目的是报告此开发。
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