On H-supplemented modules over a right perfect ring

In 1971, Koehler 11 Koehler, A. (1971). Quasi-projective and quasi-injective modules. Pac. J. Math. 36(3):713–720.Crossref], Web of Science ®] , Google Scholar]] proved a structure theorem for quasi-projective modules over right perfect rings by using results of Wu–Jans 22 Wu, L. E. T., Jans, J. P. (1967). On quasi-projectives. Illinois J. Math. 11:439–448. Google Scholar]]. Later Mohamed–Singh 17 Mohamed, S. H., Singh, S. (1977). Generalizations of decomposition theorems known over perfect rings. J. Aust. Math. Soc. Ser. A 24(4):496–510.Crossref] , Google Scholar]] studied discrete modules over right perfect rings and gave decomposition theorems for these modules. Moreover, Oshiro 18 Oshiro, K. (1983). Semiperfect modules and quasi-semiperfect modules. Osaka J. Math. 20:337–372.Web of Science ®] , Google Scholar]] deeply studied (quasi-)discrete modules over general rings. In this paper, we consider that decomposition theorems for H-supplemented modules with the condition (D₂) or (D₃) over right perfect rings.