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 On doubly stochastic $k$-potent matrices and regular matrices Bull. Korean Math. Soc. 2000 Vol. 37, No. 2, 401-409 Sung-Soo Pyo Kyungpook National University Abstract : In this paper, we determine the structure of $k$-potent elements and regular elements of the semigroup $\Omega_n$ of doubly stochastic matrices of order $n$. In connection with this, we find the structure of the matrices $X$ satisfying the equation $AXA= A$. From these, we determine a condition of a doubly stochastic matrix $A$ whose Moore-Penrose generalized inverse is also a doubly stochastic matrix. Keywords : doubly stochastic, $k-$potent, regular elements MSC numbers : 15A51 Downloads: Full-text PDF