Realizable partial multiplications in linear lattices
Izvestiya. Mathematics, Tome 1 (1967) no. 6, pp. 1153-1176 Cet article a éte moissonné depuis la source Math-Net.Ru

Voir la notice de l'article

Partial multiplication operations in linear lattices are studied. In particular, abstract characterizations of realizable partial multiplications are given. Some of the results have been presented without proofs in § 1 of $({}^4)$.
@article{IM2_1967_1_6_a0,
     author = {A. I. Veksler},
     title = {Realizable partial multiplications in linear lattices},
     journal = {Izvestiya. Mathematics},
     pages = {1153--1176},
     year = {1967},
     volume = {1},
     number = {6},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a0/}
}
TY  - JOUR
AU  - A. I. Veksler
TI  - Realizable partial multiplications in linear lattices
JO  - Izvestiya. Mathematics
PY  - 1967
SP  - 1153
EP  - 1176
VL  - 1
IS  - 6
UR  - http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a0/
LA  - en
ID  - IM2_1967_1_6_a0
ER  - 
%0 Journal Article
%A A. I. Veksler
%T Realizable partial multiplications in linear lattices
%J Izvestiya. Mathematics
%D 1967
%P 1153-1176
%V 1
%N 6
%U http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a0/
%G en
%F IM2_1967_1_6_a0
A. I. Veksler. Realizable partial multiplications in linear lattices. Izvestiya. Mathematics, Tome 1 (1967) no. 6, pp. 1153-1176. http://geodesic.mathdoc.fr/item/IM2_1967_1_6_a0/

[1] Amemiya J., “A general spectral theory in semi-ordered linear spaces”, J. Fac. Sci. Hokkaido Univ., Math., 12:3 (1953), 111–156 | MR | Zbl

[2] Birkhoff G., Pierce R. S., “Lattice-ordered rings”, Anais Acad. Brasil. ciênc, 28:1 (1956), 41–69 | MR | Zbl

[3] Veksler A. I., “O realizatsiyakh arkhimedovykh $K$-linealov”, Sib. matem. zh., 3:1 (1962), 7–16 | MR | Zbl

[4] Vekeler A. I., “Operatsii chastichnogo umnozheniya v vektornykh strukturakh”, Dokl. AN SSSR, 158:4 (1964), 759–762

[5] Vulikh B. Z., “Opredelenie proizvedeniya v lineinom poluuporyadochennom prostranstve”, Dokl. AN SSSR, 26:9 (1940), 847–851

[6] Bylikh B. Z., “Svoistva proizvedeniya i obratnogo elementa v lineinykh poluuporyadochennykh prostranstvakh”, Dokl. AN SSSR, 26:9 (1940), 852–856

[7] Vulikh B. Z., “Proizvedenie v lineinykh poluuporyadochennykh prostranstvakh i ego primenenie k teorii operatsii. I”, Matem. sb., 22:1 (1948), 27–78

[8] Vulikh B. Z., “Proizvedenie v lineinykh poluuporyadochennykh prostranstvakh i ego primenenie k teorii operatsii. II”, Matem. sb., 22:2 (1948), 267–317

[9] Bylikh B. Z., “Obobschennye poluuporyadochennye koltsa”, Matem. sb., 33:2 (1953), 343–358 | MR

[10] Bylikh B. Z., “Kharakteristicheskie svoistva proizvedeniya v lineinykh poluuporyadochennykh prostranstvakh”, Uch. zap. Leningr. gos. ped. in-ta im. A. I. Gertsena, 89 (1953), 3–8

[11] Bylikh B. Z., “O svoistve vnutrennei normalnosti obobschennykh poluuporyadochennykh kolets”, Uch. zap. Leningr. gos. ped. in-ta im. A. I. Gertsena, 166 (1958), 3–15

[12] Vulikh B. Z., “O rasprostranenii nepreryvnykh funktsii v topologicheskikh prostranstvakh”, Matem. sb., 30:1 (1952), 167–170

[13] Bylikh B. Z., Vvedenie v teoriyu poluuporyadochennykh prostranstv, Fizmatgiz, Moskva, 1961

[14] Gleason A. M., “Projective topological spaces”, Illinois J. Math., 2:4A (1958), 482–489 | MR | Zbl

[15] Johnson D. G., “On a representation theory for a class of archimedean lattice-ordered rings”, Proc. London Math. Soc., 12:46 (1962), 207–225 | DOI | MR | Zbl

[16] Domracheva G. I., Obobschennye poluuporyadochennye koltsa i ikh idealy, Dissertatsiya, Leningr. gos. ped. in-t im. A. I. Gertsena, 1955

[17] Kist J., “Representations of archimedean function rings”, Illinois J. Math., 7:2 (1963), 269–278 | MR | Zbl

[18] Krein M. G., Krein S. G., “O prostranstve nepreryvnykh funktsii, opredelennykh na bikompakte, i ego poluuporyadochennykh prostranstvakh”, Matem. sb., 13:1 (1943), 1–38 | MR | Zbl

[19] Nakano H., Modern spectral theory, Maruzen Co., Tokyo, 1950 | MR

[20] Ponomarev V. I., “O parakompaktnykh prostranstvakh i ikh nepreryvnykh otobrazheniyakh”, Dokl. AN SSSR, 143:1 (1962), 46–49 | MR | Zbl

[21] Freudental H., “Teilweise geordnete Moduln”, Proc. Acad. Amsterdam, 39 (1936), 641–651