We present new generalized Jacobson?s lemma for Drazin inverses. This extends the main results on g-Drazin inverse of Yan, Zeng and Zhu (Linear & Multilinear Algebra, 68(2020), 81-93).

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In Open Problems #3 (Summer 1991), I mentioned several analogues or extensions of Edmonds' Branching Theorem. Let 0 (G; r) be the minimum number of edges that must be deleted to make some vertex of a digraph G unreachable from r, and let (G; r) be the analogous parameter for vertex deletion. Edmonds proved that G has 0 (G; r) edge-disjoint r-branchings in G, where an r-branching is a subgraph i...

We compute the infinitesimal deformations of two families of restricted simple modular Lie algebras of Cartan-type: the Witt-Jacobson and the Special Lie algebras.

It is shown that the right-adequate duo ring with a nonzero Jacobson radical has stable range one. established class of complete matrices order 2 over elementary divisors Some classes unit-regular and clean are investigated.