Geodesic
Lambek functional representation of generalized symmetric semirings
Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 26-35.

Voir la notice de l'article provenant de la source Math-Net.Ru

The article defines almost symmetric and generalized symmetric semirings. These notions generalize symmetric semirings, as well as almost and pseudo symmetric rings. Isomorphic representations of these semirings by sections of the Lambek sheaf of semirings are obtained.
Keywords: semiring, generalized symmetric semiring, sheaf, Lambek representation. 
@article{IVM_2023_2_a1,
     author = {E.M. Vechtomov and V. V. Chermnykh},
     title = {Lambek functional representation of generalized symmetric semirings},
     journal = {Izvesti\^a vys\v{s}ih u\v{c}ebnyh zavedenij. Matematika},
     pages = {26--35},
     publisher = {mathdoc},
     number = {2},
     year = {2023},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/IVM_2023_2_a1/}
}
TY  - JOUR
AU  - E.M. Vechtomov
AU  - V. V. Chermnykh
TI  - Lambek functional representation of generalized symmetric semirings
JO  - Izvestiâ vysših učebnyh zavedenij. Matematika
PY  - 2023
SP  - 26
EP  - 35
IS  - 2
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/IVM_2023_2_a1/
LA  - ru
ID  - IVM_2023_2_a1
ER  - 
%0 Journal Article
%A E.M. Vechtomov
%A V. V. Chermnykh
%T Lambek functional representation of generalized symmetric semirings
%J Izvestiâ vysših učebnyh zavedenij. Matematika
%D 2023
%P 26-35
%N 2
%I mathdoc
%U http://geodesic.mathdoc.fr/item/IVM_2023_2_a1/
%G ru
%F IVM_2023_2_a1
E.M. Vechtomov; V. V. Chermnykh. Lambek functional representation of generalized symmetric semirings. Izvestiâ vysših učebnyh zavedenij. Matematika, no. 2 (2023), pp. 26-35. http://geodesic.mathdoc.fr/item/IVM_2023_2_a1/

[1] Golan J.S., Semirings and their applications, Kluwer Academic Publ., Dordrecht, Boston, 1999

[2] Grothendieck A., Dieudonné J.A., Éléments de Géométrie Algébrique, v. 1, Publ. Math., 4, Inst. Hautes Etudes Sci., Paris, 1960

[3] Lambek J., Lectures on rings and modules, Blaisdell Publ. Company, New York, 1966

[4] Vechtomov E.M., “Rings and sheaves”, J. Math. Sci., 74:1 (1995), 749–798

[5] Dauns J., Hofmann K.H., “The representation of biregular rings by sheaves”, Math. Z., 12:4 (1968), 3–24

[6] Koh K., “On functional representation of ring without nilpotent elements”, Can. Math. Bull., 14:3 (1971), 349–352

[7] Koh K., “On a representation of strongly harmonic ring by sheaves”, Pacif J. Math., 41:2 (1972), 459–468

[8] Hofmann K.H., “Representations of algebras by continuons sections”, Bull. Amer. Math. Soc., 78:3 (1972), 291–373

[9] Mulvey C.J., “A generalization of Gelfand duality”, J. Algebra, 56:2 (1979), 499–505

[10] Chermnykh V.V., “Puchkovye predstavleniya polukolets”, UMN, 48:5 (1993), 185–186

[11] Chermnykh V.V., “Funktsionalnye predstavleniya polukolets”, Fundament. i prikl. matem., 17:3 (2012), 111–227

[12] Lambek J., “On the Representation of Modules by Sheaves of Factor Modules”, Can. Math. Bull., 14:3 (1971), 359–368

[13] Shin G., “Prime ideals and sheaf representation of a pseudo symmetric ring”, Trans. Amer. Math. Soc., 184 (1973), 43–60

[14] Burgess W.D., Stephenson W., “Pierce sheaves of non-commutative rings”, Comm. Algebra, 4:1 (1976), 51–75

[15] Burgess W.D., Stephenson W., “An analogue of the Pierce sheaf for noncommutative rings”, Comm. Algebra, 6:9 (1978), 863–886

[16] Bredon G., Teoriya puchkov, Nauka, M., 1988