## The structure of certain operator algebras

HTML articles powered by AMS MathViewer

- by Irving Kaplansky PDF
- Trans. Amer. Math. Soc.
**70**(1951), 219-255 Request permission

## References

- A. Adrian Albert,
*Structure of algebras*, American Mathematical Society Colloquium Publications, Vol. XXIV, American Mathematical Society, Providence, R.I., 1961. Revised printing. MR**0123587** - Richard F. Arens and Irving Kaplansky,
*Topological representation of algebras*, Trans. Amer. Math. Soc.**63**(1948), 457–481. MR**25453**, DOI 10.1090/S0002-9947-1948-0025453-6
N. Bourbaki, - I. Gelfand and M. Neumark,
*On the imbedding of normed rings into the ring of operators in Hilbert space*, Rec. Math. [Mat. Sbornik] N.S.**12(54)**(1943), 197–213 (English, with Russian summary). MR**0009426** - I. M. Gel′fand and M. A. Naĭmark,
*Unitary representations of the Lorentz group*, Izvestiya Akad. Nauk SSSR. Ser. Mat.**11**(1947), 411–504 (Russian). MR**0024440** - Roger Godement,
*Théorie générale des sommes continues d’espaces de Banach*, C. R. Acad. Sci. Paris**228**(1949), 1321–1323 (French). MR**29102** - N. Jacobson,
*The radical and semi-simplicity for arbitrary rings*, Amer. J. Math.**67**(1945), 300–320. MR**12271**, DOI 10.2307/2371731 - N. Jacobson,
*A topology for the set of primitive ideals in an arbitrary ring*, Proc. Nat. Acad. Sci. U.S.A.**31**(1945), 333–338. MR**13138**, DOI 10.1073/pnas.31.10.333 - N. Jacobson,
*Structure theory for algebraic algebras of bounded degree*, Ann. of Math. (2)**46**(1945), 695–707. MR**14083**, DOI 10.2307/1969205 - Irving Kaplansky,
*Dual rings*, Ann. of Math. (2)**49**(1948), 689–701. MR**25452**, DOI 10.2307/1969052 - Irving Kaplansky,
*Groups with representations of bounded degree*, Canad. J. Math.**1**(1949), 105–112. MR**28317**, DOI 10.4153/cjm-1949-011-9 - Irving Kaplansky,
*Normed algebras*, Duke Math. J.**16**(1949), 399–418. MR**31193** - Irving Kaplansky,
*Topological representation of algebras. II*, Trans. Amer. Math. Soc.**68**(1950), 62–75. MR**32612**, DOI 10.1090/S0002-9947-1950-0032612-4 - F. J. Murray and J. Von Neumann,
*On rings of operators*, Ann. of Math. (2)**37**(1936), no. 1, 116–229. MR**1503275**, DOI 10.2307/1968693 - M. A. Naĭmark,
*Rings with involutions*, Uspehi Matem. Nauk (N.S.)**3**(1948), no. 5(27), 52–145 (Russian). MR**0027448** - John von Neumann,
*On rings of operators. Reduction theory*, Ann. of Math. (2)**50**(1949), 401–485. MR**29101**, DOI 10.2307/1969463 - D. A. Raikov,
*To the theory of normed rings with involution*, C. R. (Doklady) Acad. Sci. URSS (N.S.)**54**(1946), 387–390. MR**0019845** - C. E. Rickart,
*Banach algebras with an adjoint operation*, Ann. of Math. (2)**47**(1946), 528–550. MR**17474**, DOI 10.2307/1969091 - I. E. Segal,
*Irreducible representations of operator algebras*, Bull. Amer. Math. Soc.**53**(1947), 73–88. MR**20217**, DOI 10.1090/S0002-9904-1947-08742-5 - Hing Tong,
*On ideals of certain topologized rings of continuous mappings associated with topological spaces*, Ann. of Math. (2)**50**(1949), 329–340. MR**29083**, DOI 10.2307/1969458

*Élements de mathématique*, vol. 3,

*Topologie générale*, Actualités Scientifiques et Industrielles, no. 1045, Paris, 1948.

## Additional Information

- © Copyright 1951 American Mathematical Society
- Journal: Trans. Amer. Math. Soc.
**70**(1951), 219-255 - MSC: Primary 46.3X
- DOI: https://doi.org/10.1090/S0002-9947-1951-0042066-0
- MathSciNet review: 0042066