It is shown that, in any semigroup with involution, both the DMP inverse of Malik and Thome [Appl Math Comp. 2014;226:575–580.] and the CMP inverse of Mehdipour and Salemi [Linear Multilinear Alg. 2018;66:1046–1053.] are special cases of the Bott–Duffin $(e,f)$-inverse introduced in [Linear Algebra Appl. 2012;436:1909-1923.] It is also shown that the core inverse of O.M. Baksalary and Trenkler [Linear Multilinear Alg. 2010;58:681–697.] can (even for other pairs of generalized inverses) also be alternatively described, in three other equivalent ways, as the $(b,c)$-inverse y of a for three other choices of $(b,c)$ besides $(b,c)=(a{a}^{†},a{a}^{†})$.

结果表明，在任何具有对合的半群中，Malik 和 Thome [Appl Math Comp. 2014;226:575–580.] 和 Mehdipour 和 Salemi 的 CMP 逆 [线性多线性算法。2018;66:1046–1053.] 是 Bott-Duffin 的特例$(\mathrm{电子},F)$-inverse 在 [线性代数应用。2012;436:1909-1923.] 还显示了 OM Baksalary 和 Trenkler [线性多线性算法的核心逆。2010;58:681–697.] 也可以（即使对于其他广义逆对）也可以用其他三种等效方式替代地描述为$(b,C)$- 对a的其他三个选择的逆y$(b,C)$除了$(b,C)=(A{A}^{†},A{A}^{†})$.