On the equivalence of the ring, lattice, and semigroup of continuous functions

Author:
Melvin Henriksen

Journal:
Proc. Amer. Math. Soc. **7** (1956), 959-960

MSC:
Primary 09.3X

DOI:
https://doi.org/10.1090/S0002-9939-1956-0082490-3

MathSciNet review:
0082490

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References | Similar Articles | Additional Information

**[1]**Frank W. Anderson,*A lattice characterization of completely regular 𝐺_{𝛿}-spaces*, Proc. Amer. Math. Soc.**6**(1955), 757–765. MR**0072451**, https://doi.org/10.1090/S0002-9939-1955-0072451-1**[2]**I. Gelfand and A. N. Kolmogoroff,*On rings of continuous functions on topological spaces*, C.R. (Doklady) Acad. Sci. URSS. vol. 22 (1939) pp. 11-15.**[3]**Edwin Hewitt,*Rings of real-valued continuous functions. I*, Trans. Amer. Math. Soc.**64**(1948), 45–99. MR**0026239**, https://doi.org/10.1090/S0002-9947-1948-0026239-9**[4]**Irving Kaplansky,*Lattices of continuous functions*, Bull. Amer. Math. Soc.**53**(1947), 617–623. MR**0020715**, https://doi.org/10.1090/S0002-9904-1947-08856-X**[5]**A. N. Milgram,*Multiplicative semigroups of continuous functions*, Duke Math. J.**16**(1940), 377–383. MR**0029476****[6]**Lyle E. Pursell,*An algebraic characterization of fixed ideals in certain function rings*, Pacific J. Math.**5**(1955), 963–969. MR**0083478****[7]**Taira Shirota,*A generalization of a theorem of I. Kaplansky*, Osaka Math. J.**4**(1952), 121–132. MR**0052760****[8]**M. H. Stone,*Applications of the theory of Boolean rings to general topology*, Trans. Amer. Math. Soc.**41**(1937), no. 3, 375–481. MR**1501905**, https://doi.org/10.1090/S0002-9947-1937-1501905-7

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DOI:
https://doi.org/10.1090/S0002-9939-1956-0082490-3

Article copyright:
© Copyright 1956
American Mathematical Society