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Theory of \(x\)-ideals. (English) Zbl 0108.26002

MSC:
20M14 Commutative semigroups
20M12 Ideal theory for semigroups
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[1] K. E. Aubert, Généralisation de la théorie desr-idéaux de Prüfer-Lorenzen.C. R. Acad. Sci. Paris, 238 (1954), 214–216.
[2] K. E. Aubert,Contribution à la theorie des idéaux et à la théorie des valuations. Thèse, Paris 1957.
[3] –, Un théorème d’immersion pour une classe étendue de structures algébriques réticulées.An. Acad. Brasil. Ci., 31 (1959), 321–329.
[4] G. Birkhoff,Lattice theory. New York 1948. · Zbl 0033.10103
[5] R. Croisot & L. Lesieur,Théorie noethérienne des anneaux, des demi-groupes et des modules dans le cas non-commentatif I. Colloque d’Algèbre supérieure, Bruxelles 1956, 79–121.
[6] R. P. Dilworth &M. Ward, Residuated lattices.Trans. Amer. Math. Soc., 45 (1939), 335–354. · JFM 65.0084.01
[7] R. P. Dilworth, Non-commutative residuated lattices.Trans. Amer. Math. Soc., 46 (1939), 426–444. · Zbl 0022.10402
[8] M. L. Dubreil-Jacotin, L. Lesieur & R. Croisot,Leçons sur la théorie des treillis ... Paris 1953. · Zbl 0051.26005
[9] I. Gelfand &A. N. Kolmogoroff, On rings of continuous functions on topological spaces.Dokl. Akad. Nauk SSSR 22 (1939), 11–15. · Zbl 0021.41103
[10] P. M. Grundy, A generalization of additive ideal theory.Proc. Cambridge Philos. Soc., 38 (1942), 241–279. · Zbl 0060.06814
[11] P. R. Halmos, Algebraic logic I.Compositio Math., 12 (1956), 217–249. · Zbl 0087.24505
[12] –, Algebraic logic II.Fund. Math., 43 (1956), 255–325.
[13] J. Hashimoto, Ideal theory for lattices.Math. Japon. 2 (1952), 149–186. · Zbl 0048.25903
[14] P. Jaffard,Les systèmes d’idéaux. Dunod, Paris 1960. · Zbl 0101.27502
[15] I. Kaplansky,An introduction to differential algebra. Hermann, Paris 1957. · Zbl 0083.03301
[16] W. Krull, Idealtheorie in Ringen ohne Endlichkeitsbedingung.Math. Ann., 101 (1929), 729–744. · JFM 55.0681.01
[17] –, Axiomatische Begründung der allgemeinen Idealtheorie.Sitzungsberichte der physikalisch-medicinischen Societät zu Erlangen, 56 (1924), 47–63.
[18] –, Beiträge zur Arithmetik kommutativer Integritätsbereiche.Math. Z., 41 (1936), 545–577. · JFM 62.1105.01
[19] L. Lesieur, Sur les demi-groupes réticulés satisfaisant a une condition de chaîne.Bull. Soc. Math. France, 83 (1955), 161–193. · Zbl 0064.26102
[20] L. H. Loomis,An introduction to abstract harmonic analysis. New York 1953. · Zbl 0052.11701
[21] P. Lorenzen, Abstrakte Begründung der multiplikativen Idealtheorie.Math. Z., 45 (1939), 533–553. · JFM 65.0101.01
[22] –, Über halbgeordnete Gruppen.Math. Z., 52 (1949), 483–526. · Zbl 0035.29303
[23] –, Teilbarkeitstheorie in Bereichen.Math. Z. 55 (1952), 269–275. · Zbl 0048.01202
[24] N. H. McCoy,Rings and ideals. Carus Monograph Series No. 8, 1948.
[25] A. Monteiro, Filtros e ideais I, II.Notas de Mat., 2 & 5, Rio de Janeiro 1959.
[26] D. C. Murdoch &O. Ore, On generalized rings.Amer. J. Math., 63 (1941), 73–86. · JFM 67.0088.02
[27] H. Prüfer, Untersuchungen über Teilbarkeitseigenschaften in Körpern.J. Reine Angew. Math., 168 (1932), 1–36. · JFM 58.0147.01
[28] H. W. Raudenbush, Ideal theory and algebraic differential equations.Trans. Amer. Math. Soc., 36 (1934), 361–368. · Zbl 0009.10004
[29] J. F. Ritt,Differential Algebra. Colloquium Publications No. 33. New York 1950. · Zbl 0037.18501
[30] J. F. Ritt &H. W. Raudenbush, Ideal theory and algebraic difference equations.Trans. Amer. Math. Soc., 46 (1939), 445–452. · JFM 65.0105.02
[31] E. Schenkman, The similarity between the properties of ideals in commutative rings and the properties of normal subgroups in groups.Proc. Amer. Math. Soc., 9 (1958), 375–381. · Zbl 0089.01402
[32] M. H. Stone, A general theory of spectra I & II.Proc. Nat. Acad. Sci. U.S.A., 26–27 (1940–1941), 280–283 and 83–87. · Zbl 0063.07208
[33] B. L. van der Waerden,Algebra II, vierte Auflage 1959.
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