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 Cet article a éte moissonné depuis la source Math-Net.Ru

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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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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/

[1] Pierce R.S., “Modules over commutative regular rings”, Mem. Amer. Math. Soc., 70 (1967), 1–112 | MR

[2] Tuganbaev A.A., Teoriya kolets. Arifmeticheskie moduli i koltsa, MTsNMO, M., 2009, 472 pp.

[3] Tyukavkin D.V., Pirsovskie puchki dlya kolets s involyutsiei, Dep. VINITI # 4346-82, Izd-vo MGU, M., 1982, 64 pp.

[4] Carson A.B., “Representation of regular rinds of finite index”, J. Algebra, 39:2 (1976), 512–526 | DOI | MR | Zbl

[5] Dauns J., Hofmann K.H., “The representation of biregular rings by sheaves”, Math. Z., 91:2 (1966), 103–123 | DOI | MR | Zbl

[6] Burgess W.D., Stephenson W., “Rings all of whose Pierce stalks are local”, Canad. Math. Bull., 22:2 (1979), 159–164 | DOI | MR | Zbl

[7] Burgess W.D., Stephenson W., “Pierce sheaves of non–commutative rings”, Comm. Algebra, 39 (1976), 512–526 | DOI | MR

[8] Burgess W.D., Stephenson W., “An analogue of the Pierce sheaf for non–commutative rings”, Comm. Algebra, 6:9 (1978), 863–886 | DOI | MR | Zbl

[9] Cignoli R., “The lattice of global sections of sheaves of chains over Boolean spaces”, Algebra Universalis, 8:3 (1978), 357–373 | DOI | MR | Zbl

[10] Comer S.D., “Representation by algebras of sections over Boolean spaces”, Pacific. Math., 38 (1971), 29–38 | DOI | MR | Zbl

[11] Georgescu G., “Pierce representations of distributive lattices”, Kobe J. Math., 10:1 (1993), 1–11 | MR | Zbl

[12] Keimel K., “The representation of lattice ordered groups and rings by sections in sheaves”, Lectures on the Applications of Sheaves to Ring Theory, Lect. Notes Math., 248, Springer, Berlin, 1971, 1–98 | DOI | MR

[13] Chermnykh V.V., “Puchkovye predstavleniya polukolets”, Uspekhi mat. nauk, 48:5 (1993), 185–186 | MR | Zbl

[14] Chermnykh V.V., “Funktsionalnye predstavleniya polukolets”, Fundament. i prikl. matematika, 17:3 (2012), 111–227 | MR | Zbl

[15] Bredon G., Teoriya puchkov, Nauka, M., 1988, 312 pp. | MR

[16] Vechtomov E.M., Funktsionalnye predstavleniya kolets, Izd-vo MPGU, M., 1993, 190 pp. | MR