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New determinants and the Cayley-Hamilton Theorem for matrices over Lie nilpotent rings
We construct the so-called right adjoint sequence of an $n\times n$ matrix over an arbitrary ring. For an integer $m\geq 1$ the right $m$-adjoint and the right $m$-determinant of a matrix is defined by the use of this sequence. Over $m$-Lie nilpotent rings a considerable part of the classical determinant …