Geodesic
Extension of Congruences on Semirings of Continuous Functions
Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 803-816

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The lattices of congruences of semirings and semifields of continuous nonnegative functions over an arbitrary topological space are studied. It is proved that congruences of the semifield of continuous positive functions can be extended to congruences of the semiring of continuous nonnegative functions.
Keywords: semiring of continuous nonnegative functions, semifield of continuous positive functions, idempotent semiring (semifield), lattice of congruences. 
@article{MZM_2009_85_6_a0,
     author = {E. M. Vechtomov and D. V. Chuprakov},
     title = {Extension of {Congruences} on {Semirings} of {Continuous} {Functions}},
     journal = {Matemati\v{c}eskie zametki},
     pages = {803--816},
     publisher = {mathdoc},
     volume = {85},
     number = {6},
     year = {2009},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a0/}
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E. M. Vechtomov; D. V. Chuprakov. Extension of Congruences on Semirings of Continuous Functions. Matematičeskie zametki, Tome 85 (2009) no. 6, pp. 803-816. http://geodesic.mathdoc.fr/item/MZM_2009_85_6_a0/