Geodesic
Reduced Rickart semirings and their functional representations
Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 2, pp. 205-215

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In this paper, we consider reduced semirings with supplementary conditions of annihilators, namely these are Rickart and weakly Rickart semirings. The main aim of the paper is to study functional representations of semirings. We build two sheaves of semirings and prove that a reduced Rickart semiring is presented by sections of these sheaves. 
@article{FPM_2007_13_2_a9,
     author = {V. V. Chermnykh},
     title = {Reduced {Rickart} semirings and their functional representations},
     journal = {Fundamentalʹna\^a i prikladna\^a matematika},
     pages = {205--215},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2007},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a9/}
}
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V. V. Chermnykh. Reduced Rickart semirings and their functional representations. Fundamentalʹnaâ i prikladnaâ matematika, Tome 13 (2007) no. 2, pp. 205-215. http://geodesic.mathdoc.fr/item/FPM_2007_13_2_a9/