Geodesic
Functional representations of lattice-ordered semirings. II
Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 677-684.

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

The article considers the lattice-ordered semirings ($drl$-semirings). Two sheaves of $drl$-semirings are constructed. The first sheaf is based on prime spectrum of $l$-ideals. The idea of construction is close to the well-known sheaf of germs of continuous functions. The second sheaf resembles Pierce's sheaf of abstract rings or semirings. Its basis space is Boolean space of maximal ideals of the lattice of complemented $l$-ideals from $drl$-semiring. The main results are theorems on representations of an $l$-semiprime and an arbitrary $drl$-semirings by sections of corresponding sheaves.
Keywords: lattice-ordered semiring, sheaf, sheaf representation. 
@article{SEMR_2018_15_a17,
     author = {O. V. Chermnykh},
     title = {Functional representations of lattice-ordered semirings. {II}},
     journal = {Sibirskie \`elektronnye matemati\v{c}eskie izvesti\^a},
     pages = {677--684},
     publisher = {mathdoc},
     volume = {15},
     year = {2018},
     language = {ru},
     url = {http://geodesic.mathdoc.fr/item/SEMR_2018_15_a17/}
}
TY  - JOUR
AU  - O. V. Chermnykh
TI  - Functional representations of lattice-ordered semirings. II
JO  - Sibirskie èlektronnye matematičeskie izvestiâ
PY  - 2018
SP  - 677
EP  - 684
VL  - 15
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/SEMR_2018_15_a17/
LA  - ru
ID  - SEMR_2018_15_a17
ER  - 
%0 Journal Article
%A O. V. Chermnykh
%T Functional representations of lattice-ordered semirings. II
%J Sibirskie èlektronnye matematičeskie izvestiâ
%D 2018
%P 677-684
%V 15
%I mathdoc
%U http://geodesic.mathdoc.fr/item/SEMR_2018_15_a17/
%G ru
%F SEMR_2018_15_a17
O. V. Chermnykh. Functional representations of lattice-ordered semirings. II. Sibirskie èlektronnye matematičeskie izvestiâ, Tome 15 (2018), pp. 677-684. http://geodesic.mathdoc.fr/item/SEMR_2018_15_a17/

[1] V. V. Chermnykh, O. V. Chermnykh, “Functional representations of lattice-ordered semirings”, Siberian Electronic Mathematical Reports, 14 (2017), 946–971 | MR | Zbl

[2] K. Keimel, “The representation of lattice ordered groups and rings by sections in sheaves”, Lect. Notes Math., 248, 1971, 1–98 | DOI | MR | Zbl

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

[4] V. V. Chermnykh, “Functional representations of semirings”, Fundament. i prikl. matemat., 17:3 (2012), 111–227 | MR | Zbl

[5] P. R. Rao, “Lattice ordered semirings”, Math. Sem. Notes, Kobe Univ., 9 (1981), 119–149 | MR | Zbl

[6] B. A. Davey, “Sheaf spaces and sheaves of universal algebras”, Math. Z., 134:4 (1973), 275–290 | DOI | MR | Zbl

[7] L. Fuchs, Partially ordered algebraic systems, Pergamon Press, Oxford–London–New York–Paris, 1963 | MR | Zbl

[8] G. Birkhoff, R. S. Pierce, “Lattice-ordered rings”, An. Acad. Brasil. Ci., 28 (1956), 41–69 | MR | Zbl

[9] J. E. Diem, “A radical for lattice-ordered ring”, Pacific J. Math., 25:1 (1968), 71–82 | DOI | MR | Zbl

[10] G. Birkhoff, Lattice Theory, Amer. Math. Soc., Providence, R.I., 1967 | MR | Zbl