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. 
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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/

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