| Matrix algebra is an important branch of algebra. It has wide applications in differential geometry, graph theory, computer, quantum mechanics, control theory, economics and so on. Linear preserver problem (LPP for short) is one of the most active research areas in matrix theory. It mainly concerns the charac-terizations of linear operators between matrix space that leave certain functions, relations, subsets, etc., invariant. In this paper we study several classes of linear operators that preserve certain invariant over semiring. The main results are as follows:1. We characterize surjective linear operators that preserve {1}-inverses over the binary Boolean algebra, the chain semiring, the nonnegative intergers semiring and the nonnegative reals semiring, respectively. Based on obtained results, We get forms of surjective linear operators that preserve {1}-inverses over general Boolean algebra and direct product of some special semirings, re-spectively.2. We characterize surjective linear operators that preserve orthogonality over entire antirings. Based on obtained results, We give forms of surjective linear operators that preserve orthogonality over the general Boolean algebra and direct product of entire antirings, respectively.3. We characterize surjective linear operators that preserve Green’s relations over the binary Boolean algebra. Based on obtained results, We get forms of sur-jective linear operators that preserve Green’s relations over the general Boolean algebra and direct product of copies of binary Boolean algebra, respectively. |
