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Unital embedding and complexifications of F-algebras. (English) Zbl 0494.06010


MSC:

06F20 Ordered abelian groups, Riesz groups, ordered linear spaces
06F25 Ordered rings, algebras, modules
46A40 Ordered topological linear spaces, vector lattices

References:

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[2] Bigard, A., Keimel, K.: Sur les endomorphismes conservant les polaires d’un groupe réticulé archimédien. Bull. Soc. Math. France97, 381-398 (1969) · Zbl 0215.34203
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[8] Horne, J.G. jr.: OnO ?-ideals inC(X). Proc. Amer. Math. Soc.9, 511-518 (1958). · Zbl 0093.12504
[9] Huijsmans, C.B., de Pagter, B.: Onz-ideals andd-ideals in riesz spaces II. Indag. Math.42, 391-408 (1980) · Zbl 0451.46003
[10] Huijsmans, C.B., de Pagter, B.: Ideal theory inf-algebras. Trans. Amer. Math. Soc.269, 225-245 (1982) · Zbl 0483.06009
[11] Johnson, D.G.: A structure theory for a class of lattice-ordered rings. Acta Math.104, 163-215 (1960) · Zbl 0094.25305 · doi:10.1007/BF02546389
[12] Johnson, D.G.: The completion of an Archimedeanf-ring. J. London Math. Soc.40, 493-496 (1965) · Zbl 0131.03404 · doi:10.1112/jlms/s1-40.1.493
[13] Lotz, H.P.: Über das Spektrum positiver Operatoren. Math. Z.108, 15-32 (1968) · Zbl 0179.18002 · doi:10.1007/BF01110453
[14] Luxemburg, W.A.J.: Some aspects of the theory of Riesz spaces. The University of Arkansas Lecture Notes in Mathematics4, Fayetteville, 1979
[15] Luxemburg, W.A.J., Zaanen, A.C.: Riesz Spaces I. Amsterdam-London: North Holland 1971 · Zbl 0231.46014
[16] Luxemburg, W.A.J., Zaanen, A.C.: The linear modulus of an order bounded linear transformation I. Indag. Math.33, 422-434 (1971) · Zbl 0227.47018
[17] Mittelmeyer, G., Wolff, M.: Über den Absolutbetrag auf komplexen Vektorverbänden. Math. Z.137, 87-92 (1974) · Zbl 0284.46010 · doi:10.1007/BF01213937
[18] Pagter, B. de:f-Algebras and Orthomorphisms. Thesis, Leiden 1981
[19] Schaefer, H.H.: Banach lattice and positive operators. Die Grundlehren der Mathematischen Wissenschaften215, Berlin-Heidelberg-New York. Springer 1974 · Zbl 0296.47023
[20] Steinberg, S.A.: On lattice-ordered rings in which the square of every element is positive. J. Austral. Math. Soc. Ser. A 22, 362-370 (1976) · Zbl 0352.06017 · doi:10.1017/S1446788700014804
[21] Whitley, W.T.: Another characterization of semiprime ideals inC(X). Amer. Math. Monthly83, 349-350 (1976) · Zbl 0324.54012 · doi:10.2307/2318645
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