Geodesic
Semirings close to regular and their Pierce stalks
Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 213-221

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We investigate Pierce stalks of semirings and the properties of semirings that grow from properties of the stalks. Objects of study are semirings with nontrivial algebra of idempotents, namely, biregular and Rickart semirings with additional conditions. We obtain characterizations of such semirings in terms of the properties of their Pierce stalks and Pierce sheaves.
Keywords: rickart semiring, biregular semiring, pierce stalk, pierce sheaf of semiring. 
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     title = {Semirings close to regular and their {Pierce} stalks},
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R. V. Markov; V. V. Chermnykh. Semirings close to regular and their Pierce stalks. Trudy Instituta matematiki i mehaniki, Trudy Instituta Matematiki i Mekhaniki UrO RAN, Tome 21 (2015) no. 3, pp. 213-221. http://geodesic.mathdoc.fr/item/TIMM_2015_21_3_a22/