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Linear Operators Strongly Preserving Polynomial Equations Over Antinegative Semirings, Sang-Gu Lee

All Graduate Theses and Dissertations, Spring 1920 to Summer 2023

We characterized the group of linear operators that strongly preserve r-potent matrices over the binary Boolean semiring, nonbinary Boolean semirings, and zero-divisor free antinegative semirings. We extended these results to show that linear operators that strongly preserve r-potent matrices are equivalent to those linear operators that strongly preserve the matrix polynomial equation p(X) = X. where p(X) = X^r₁ + X^r₂ + ... + X^r_t and r₁>r₂>...>r_t≥2.

In addition, we characterized the group of linear operators that strongly preserve r-cyclic matrices over the same semirings. We …