Geodesic
The determinability of compacts by lattices of ideals and congruencies of semirings of continuous $[0,1]$-valued functions on them
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 87-91

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We consider an idempotent semiring of continuous $[0,1]$-valued functions defined on a compact $X$ with the usual multiplication and addition $\max$. We prove the determinability of $X$ by the lattice of ideals and the lattice of congruencies of the indicated semiring.
Keywords: semiring, unit interval, compact, semiring of continuous functions, lattice of ideals, lattice of congruencies. 
@article{IVM_2012_1_a11,
     author = {E. M. Vechtomov and E. N. Lubyagina},
     title = {The determinability of compacts by lattices of ideals and congruencies of semirings of continuous $[0,1]$-valued functions on them},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {87--91},
     publisher = {mathdoc},
     number = {1},
     year = {2012},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2012_1_a11/}
}
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E. M. Vechtomov; E. N. Lubyagina. The determinability of compacts by lattices of ideals and congruencies of semirings of continuous $[0,1]$-valued functions on them. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 1 (2012), pp. 87-91. http://geodesic.mathdoc.fr/item/IVM_2012_1_a11/