Geodesic
Maps that strongly preserve $\lambda$-scrambling matrices
Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 231-243

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In this paper, it is proved that for $\lambda > 1$, an additive map that strongly preserves the set of $\lambda$-scrambling matrices over $\mathbf{B}$ is a bijection. The general form of such a map over any antinegative commutative semiring with identity and without zero divisors is characterized. 
@article{ZNSL_2019_482_a15,
     author = {A. M. Maksaev},
     title = {Maps that strongly preserve $\lambda$-scrambling matrices},
     journal = {Zapiski Nauchnykh Seminarov POMI},
     pages = {231--243},
     publisher = {mathdoc},
     volume = {482},
     year = {2019},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a15/}
}
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A. M. Maksaev. Maps that strongly preserve $\lambda$-scrambling matrices. Zapiski Nauchnykh Seminarov POMI, Computational methods and algorithms. Part XXXII, Tome 482 (2019), pp. 231-243. http://geodesic.mathdoc.fr/item/ZNSL_2019_482_a15/