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Ward, Morgan; Dilworth, R. P.

Residuated lattices. (English) Zbl 0021.10801

Trans. Am. Math. Soc. 45, 335-354 (1939).
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Keywords:

Group theory, lattices
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\textit{M. Ward} and \textit{R. P. Dilworth}, Trans. Am. Math. Soc. 45, 335--354 (1939; Zbl 0021.10801)
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References:

[1] Garrett Birkhoff On the combination of sub-algebras, Proceedings of the Cambridge Philosophical Society, vol. 39 (1933), pp. 441-464. · Zbl 0007.39502
[2] -On the structure of abstract algebras, ibid., vol. 41 (1935), pp. 433-454. · Zbl 0013.00105
[3] Garrett Birkhoff, Combinatorial relations in projective geometries, Ann. of Math. (2) 36 (1935), no. 3, 743 – 748. · JFM 61.0593.01
[4] Garrett Birkhoff, On the Lattice theory of ideals, Bull. Amer. Math. Soc. 40 (1934), no. 8, 613 – 619. · JFM 60.0093.01
[5] R. Dedekind Ueber die von drei Moduln erzeugte Dualgruppe, Gesammelte mathematische Werke, vol. 2, 1931, paper 30, pp. 236-271.
[6] R. P. Dilworth, Abstract residuation over lattices, Bull. Amer. Math. Soc. 44 (1938), no. 4, 262 – 268. · Zbl 0018.34104
[7] Fritz Klein-Barmen, Dedekindsche und distributive Verbände, Math. Z. 41 (1936), no. 1, 261 – 280 (German). · JFM 62.0089.02
[8] G. Köthe Die Theorie der Verbände..., Jahresbericht der deutschen Mathematiker-Vereinigung, vol. 47 (1937), pp. 125-142. · JFM 63.0868.02
[9] Krull Axiomatische Begründung der allgemeinen Idealtheorie, Sitzungsberichte der physikalischmedicinischen Societät zu Erlangen, vol. 56 (1924), pp. 47-63. · JFM 50.0073.02
[10] Oystein Ore, On the foundation of abstract algebra. I, Ann. of Math. (2) 36 (1935), no. 2, 406 – 437. · JFM 61.0111.09
[11] B. L. Van Der Waerden Moderne Algebra, vol. 2, Berlin, 1931. · Zbl 0002.00804
[12] M. Ward and R. P. Dilworth Residuated lattices, Proceedings of the National Academy of Sciences, vol. 24 (1938), pp. 162-164. · Zbl 0018.29003
[13] Morgan Ward, Residuation in structures over which a multiplication is defined, Duke Math. J. 3 (1937), no. 4, 627 – 636. · Zbl 0018.19903
[14] Morgan Ward, Structure residuation, Ann. of Math. (2) 39 (1938), no. 3, 558 – 568. · Zbl 0019.28902
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