Geodesic
Representation of ordered projection semigroups
Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 552-568 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

This paper studies the following relations on a semigroup of functions $(\Phi,\circ)$: the relation $\subset$ of inclusion of functions (i.e. $f\subset\varphi$ if the function $\varphi$ is an extension of the function $f$), and the relations $\lceil$ and $\lfloor$ of inclusion of the first and second projections, respectively (i.e. inclusions of the domains of definition or the ranges of values of the functions). Necessary and sufficient conditions are found for an algebraic system $G$ to be isomorphic to a semigroup of single-valued functions taken together with the relations $\subset$, $\lceil$ and $\lfloor$. Bibliography: 23 titles. 
@article{SM_1971_13_4_a3,
     author = {B. M. Shain},
     title = {Representation of ordered projection semigroups},
     journal = {Sbornik. Mathematics},
     pages = {552--568},
     year = {1971},
     volume = {13},
     number = {4},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/SM_1971_13_4_a3/}
}
TY  - JOUR
AU  - B. M. Shain
TI  - Representation of ordered projection semigroups
JO  - Sbornik. Mathematics
PY  - 1971
SP  - 552
EP  - 568
VL  - 13
IS  - 4
UR  - http://geodesic.mathdoc.fr/item/SM_1971_13_4_a3/
LA  - en
ID  - SM_1971_13_4_a3
ER  - 
%0 Journal Article
%A B. M. Shain
%T Representation of ordered projection semigroups
%J Sbornik. Mathematics
%D 1971
%P 552-568
%V 13
%N 4
%U http://geodesic.mathdoc.fr/item/SM_1971_13_4_a3/
%G en
%F SM_1971_13_4_a3
B. M. Shain. Representation of ordered projection semigroups. Sbornik. Mathematics, Tome 13 (1971) no. 4, pp. 552-568. http://geodesic.mathdoc.fr/item/SM_1971_13_4_a3/

[1] E. S. Lyapin, Polugruppy, Nauka, Moskva, 1960 | MR

[2] V. V. Vagner, “Predstavlenie uporyadochennykh polugrupp”, Matem. sb., 38(80) (1956), 203–240 | MR | Zbl

[3] V. V. Vagner, “Polugruppy chastichnykh preobrazovanii s simmetrichnym otnosheniem tranzitivnosti”, Izv. VUZ'ov, Matematika, 1957, no. 1, 81–88 | MR | Zbl

[4] K. Menger, “The algebra of functions: past, present, future”, Rend. Mat., 20:3–4 (1961), 400–430 | MR

[5] S. Ginsburg, An introduction to mathematical machine theory, Addison–Wesley Co., Reading, Mass., 1962 | MR | Zbl

[6] B. Schweizer, A. Sklar, “The algebra of functions. I”, Math. Ann., 139:5 (1960), 366–382 ; “II”, ibid., 143:5 (1961), 440–447 ; “III”, ibid., 161:3 (1966), 171–196 | DOI | MR | Zbl | MR | Zbl | MR

[7] B. Schweizer, A. Sklar, “Function systems”, Math. Ann., 172:1 (1967), 1–16 | DOI | MR | Zbl

[8] B. M. Shain, “Predstavlenie uporyadochennykh polugrupp”, Uspekhi matem. nauk, XVII:6(108) (1962), 200–201

[9] B. M. Shain, “Predstavlenie uporyadochennykh polugrupp”, Matem. sb., 65(107) (1964), 188–197

[10] B. M. Shain, “K teorii polugrupp preobrazovanii”, Trudy molodykh uchenykh, vyp. matem., 1964, 120–122, Saratov

[11] B. M. Shain, “Vmeschenie polugrupp v obobschennye gruppy”, Matem. sb., 55(97) (1961), 379–400

[12] B. M. Shain, “Predstavlenie polugrupp”, Rezyume soobsch. i dokl. 1-go Vsesoyuznogo simpoz. po teorii polugrupp, Sverdlovsk, 1969, 79–89

[13] B. M. Shain, “Transformativnye polugruppy preobrazovanii”, Matem. sb., 71(113) (1966), 65–82

[14] B. M. Shain, Algebry otnoshenii, Avtoreferat doktorskoi dissertatsii, 1965

[15] B. M. Schein, “Relation algebras”, Bull. Acad, polon. Sci., Ser. Sci. Math., Astr. el Phys., 13:1 (1966), 1–5 | MR

[16] B. M. Shain, “Algebry otnoshenii”, Dokl., soobsch., rezyume Mezhvuzovsk. nauchn. simpoz. po obschei algebre, Tartu, 1966, 130–168

[17] B. M. Schein, “Relation algebras and function semigroups”, Semigroup Forum, 1:1 (1970), 1–62 | DOI | MR | Zbl

[18] B. M. Shain, “Restriktivno-multiplikativnye algebry preobrazovanii”, Izv. VUZ'ov, Matematika, 1970, no. 4(95), 91–102

[19] V. N. Salii, “Proektsionnye polugruppy”, Izv. VUZ'ov, Matematika, 1966, no. 3(52), 144–149 | MR | Zbl

[20] V. N. Salii, “Relyativizirovannye polugruppy preobrazovanii, soderzhaschie pervoe proektsionnoe otnoshenie $\chi$”, Izv. VUZ'ov, Matematika, 1969, no. 8(87), 89–103 | MR | Zbl

[21] V. Schein, “On some problems in the theory of partial automata”, Kybernetika (Prague), 5:1 (1969), 44–49 | MR | Zbl

[22] B. M. Schein, “Linearly fundamentally ordered semigroups”, Colloq. Math., 24:2 (1970) | MR

[23] B. M. Shain, “O nekotorykh komitantakh polugrupp binarnykh otnoshenii”, Matem. zapiski UrGu, 5:1 (1965), 73–91 | MR