Publications Meetings The Profession Membership Programs Math Samplings Policy & Advocacy In the News About the AMS
|
   
Mobile Device Pairing
Bulletin of the American Mathematical Society
Bulletin of the American Mathematical Society
ISSN 1088-9485(e) ISSN 0273-0979(p)

     

Totally ordered commutative semigroups

Author(s): A. H. Clifford
Journal: Bull. Amer. Math. Soc. 64 (1958), 305-316.
MathSciNet review: 0100641
Retrieve article in: PDF

References | Additional information

References:

1.
Jean Aczél, Sur les opérations définies pour nombres réels, Bull. Soc. Math. France, vol. 76 (1948) pp. 59-64. MR 29946
2.
N. G. Alimov, On ordered semigroups, Izv. Akad. Nauk SSSR. Ser. Mat. vol. 14 (1950) pp. 569-576 (Russian); Math. Rev. vol. 12, p. 480. Translated into English by R. P. Rich, Applied Physics Laboratory, Johns Hopkins University, Silver Spring, Maryland. MR 38990
3.
C. G. Chehata, On an ordered semigroup, J. London Math. Soc. vol. 28 (1953) pp. 353-356. MR 54590
4.
A. H. Clifford, Naturally totally ordered commutative semigroups, Amer. J. Math. vol. 76 (1954) pp. 631-646. MR 62118
5.
A. H. Clifford, Connected ordered topological semigroups with idempotent endpoints I, Trans. Amer. Math. Soc., vol. 88 (1958) pp. 80-98. MR 95221
6.
A. H. Clifford, Completion of semi-continuous ordered commutative semigroups, Duke Math. J., to appear. MR 101276
7.
Haskell Cohen and L. I. Wade, Clans with zero on an interval, Trans. Amer. Math. Soc. vol. 88 (1958) pp. 523-535. MR 95222
8.
W. M. Faucett, Compact semigroups irreducibly connected between two idempotents, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 741-747. MR 71712
9.
W. M. Faucett, Topological semigroups and continua with cut points, Proc. Amer. Math. Soc. vol. 6 (1955) pp. 748-756. MR 71713
10.
Andrew M. Gleason, Arcs in locally compact groups, Proc. Nat. Acad. Sci. vol. 36 (1950) pp. 663-667. MR 38356
11.
O. Hölder, Die Axiome der Quantität and die Lehre vom Mass, Ber. uber d. Verh. d. K. Sächsischen Ges. d. Wiss. zu Leipzig, Math.-Phys. Cl. vol. 53 (1901) pp. 1-64.
12.
E. V. Huntington, A complete set of postulates for the theory of absolute continuous magnitude, Trans. Amer. Math. Soc. vol. 3 (1902) pp. 264-279. MR 1500598
13.
E. V. Huntington, Complete sets of postulates for the theories of positive integral and positive rational numbers, Trans. Amer. Math. Soc. vol. 3 (1902) pp. 280-284. MR 1500599
14.
F. Klein-Barmen, Über gewisse Halbverbände und kommutative Semigruppen II, Math. Z. vol. 48 (1942-1943) pp. 715-734. MR 8600
15.
F. Klein-Barmen, Ein Beitrag zur Theorie der linearen Holoide, Math. Z. vol. 51 (1947-1949) pp. 355-366. MR 27767
16.
Paul S. Mostert and Allen L. Shields, On the structure of semigroups on a compact manifold with boundary, Ann. of Math. vol. 65 (1957) pp. 117-143. MR 84103
17.
Paul S. Mostert and Allen L. Shields, On a class of semigroups on E, Proc. Amer. Math. Soc. vol. 7 (1956) pp. 729-734. MR 78646
18.
O. Nakada, Partially ordered abelian semigroups I. On the extension of the strong partial order defined on abelian semigroups, J. Fac. Sci. Hokkaido Univ. vol. 11 (1951) pp. 181-189. MR 47030
19.
O. Nakada, Partially ordered abelian semigroups II. On the strongness of the linear order defined on abelian semigroups, J. Fac. Sci. Hokkaido Univ. vol. 12 (1952) pp. 73-86. MR 54591
20.
Dov Tamari, Caractérisation des semi-groupes à un paramètre, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 1092-1094. MR 28844
21.
Dov Tamari, Groupoïdes reliés et demi-groupes ordonnés, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 1184-1186. MR 28845
22.
Dov Tamari, Groupoïdes ordonnés. L'ordre lexicographique pondéré, C. R. Acad. Sci. Paris vol. 228 (1949) pp. 1909-1911. MR 30525
23.
Dov Tamari, Ordres pondérés. Caractérisation de l'ordre naturel comme l'ordre du semi-groupe multiplicatif des nombres naturels, C. R. Acad. Sci. Paris vol. 229 (1949) pp. 98-100. MR 30963
24.
A. A. Vinogradov, On the theory of ordered semigroups, Ivanov. Gos. Ped. Inst. Uč. Zap. Fiz.-Mat. Nauki, vol. 4 (1953) pp. 19-21 (Russian); Math. Rev. vol. 17, p. 710. MR 75215
25.
M. Yamada, Regularly totally ordered semigroups I, Science Reports of Shimane University, 1957, pp. 14-23.
25a. V. S. Krishnan, Les algèbres partiellement ordonnées et leurs extensions, Bull. Soc. Math. France vol. 73 (1950) pp. 235-263. MR 43071

26.
Garrett Birkhoff, Lattice theory, Amer. Math. Soc. Colloquium Publications, vol. 25, rev. ed., 1948. MR 29876
27.
A. B. Clarke, On the representation of cardinal algebras by directed sums, Trans. Amer. Math. Soc. (to appear). MR 106199
28.
D. Rees, On semi-groups, Proc. Cambridge Philos. Soc. vol. 36 (1940) pp. 387-400. MR 2893
29.
Alfred Tarski, Cardinal algebras, Oxford University Press, 1949. MR 29954
30.
A. D. Wallace, The structure of topological semigroups, Bull. Amer. Math. Soc. vol. 61 (1955) pp. 95-112. MR 67907


Additional Information:

DOI: 10.1090/S0002-9904-1958-10221-9
PII: S 0002-9904(1958)10221-9




AMS and Social Media LinkedIn Facebook Podcasts Twitter YouTube RSS Feeds Blogs Wikipedia