On nilpotency of matrices over antirings
An antiring is a semiring which is zerosumfree (i.e., \(a+b=0\) implies \(a=b=0\) for any \(a,b\) in this semiring). The author studies the nilpotency of matrices over commutative antirings. He provides some properties and characterizations of the nilpotent matrices in terms of principal permanental minors, main diagonals and permanental adjoint matrices. When a family of matrices are simultaneously considered, he establishes some characterizations of the simultaneous nilpotency for a family of matrices.
scientific article; zbMATH DE number 5804411
scientific article