Geodesic
About prime ideals in semirings of continuous function with values in unit segment
Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 12-18

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The properties of the prime ideals in semirings of the continuous functions on topological spaces with values in [0,1] are researches. Maximal ideals of the semirings of continuous [0,1]-valued functions are described. The characterizations of the compacts are received in terms of semiring of the functions. It is shown that the theory of ideals in considered semirings differs from the case of rings of continuous functions.
Keywords: semiring, unit interval, compact, semiring of the continuous functions, prime ideal of the semiring. 
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     author = {E. M. Vechtomov and E. N. Lubiagina},
     title = {About prime ideals in semirings of continuous function with values in unit segment},
     journal = {Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹ\^uternye nauki},
     pages = {12--18},
     publisher = {mathdoc},
     number = {2},
     year = {2011},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/VUU_2011_2_a1/}
}
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E. M. Vechtomov; E. N. Lubiagina. About prime ideals in semirings of continuous function with values in unit segment. Vestnik Udmurtskogo universiteta. Matematika, mehanika, kompʹûternye nauki, no. 2 (2011), pp. 12-18. http://geodesic.mathdoc.fr/item/VUU_2011_2_a1/