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Maximal ideals in generalized partially ordered rings of continuous functions with a multiplication unit. (English. Russian original) Zbl 0233.46070

Sib. Math. J. 12(1971), 501-508 (1972); translation from Sib. Mat. Zh. 12, 707-717 (1971).

MSC:

46J20 Ideals, maximal ideals, boundaries
46H10 Ideals and subalgebras
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References:

[1] B. Z. Vulikh, ?Definition of the product in a linear partially ordered space,? Dokl. AN SSSR,26, 847-852 (1940).
[2] B. Z. Vulikh, ?Properties of the product and the inverse element in linear partially ordered spaces,? Dokl. AN SSSR,26, 852-856 (1940).
[3] B. Z. Vulikh, ?The product in linear partially ordered spaces and its application to the theory of operations. I,? Matem. Sb.,22, No. 1, 27-78 (1948).
[4] B. Z. Vulikh, ?The product in linear partially ordered spaces and its application to the theory of operations. II,? Matem. Sb.,22, No. 2, 267-317 (1948).
[5] B. Z. Vulikh, ?Generalized partially ordered rings,? Matem. Sb.,33, No. 2, 343-358 (1953).
[6] B. Z. Vulikh, ?Characteristic properties of the product in linear partially ordered spaces,? Uch. Zap. Leningr. Gos. Ped. Inst. im. A. I. Gertsen,89, 3-8 (1953).
[7] B. Z. Vulikh, ?On the property of intrinsic normality of generalized partially ordered rings,? Uch. Zap. Leningr. Gos. Ped. Inst. im. A. I. Gertsen,166, 3-15 (1958).
[8] B. Z. Vulikh, Introduction to the Theory of Partially Ordered Spaces [in Russian], Fizmatgiz, Moscow (1961). · Zbl 0101.08501
[9] G. I. Domracheva, ?Generalized partially ordered rings,? Uch. Zap. Novgorodsk. Gos. Ped. Inst.,1, No. 1, 51-60 (1960).
[10] I. M. Gel’fand and A. N. Kolmogorov, ?On rings of continuous functions on topological spaces,? Dokl. AN SSSR,22, No. 1, 11-15 (1939).
[11] L. Gillman and M. Jerison, Rings of Continuous Functions, Princeton (1960). · Zbl 0093.30001
[12] G. I. Domracheva, ?Ideals in normal subrings of a ring of continuous functions,? Uch. Zap. Novgorodsk. Gos. Ped. Inst. im. A. I. Gertsen,166, 29-38 (1958).
[13] G. Ya. Ivanova, ?Characterization of maximal ideals in normal subrings of a ring of continuous functions,? Uch. Zap. Novgorodsk. Gos. Ped. Inst.,7, 28-36 (1966).
[14] G. Ya. Ivanova, ?Ideals in generalized partially ordered rings of continuous functions,? Uch. Zap. Novgorodsk. Gos. Ped. Inst.,7, 17-27 (1966).
[15] G. I. Domracheva, ?Partially ordered fields,? Uch. Zap. Novgorodsk. Gos. Ped. Inst.,1, No. 1, 61-69 (1960).
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