Book Review
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MathSciNet review:
1567273
Full text of review:
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Book Information:
Author:
K. R. Goodearl
Title:
Von Neumann regular rings
Additional book information:
Monographs and Studies in Mathematics, No. 4, Pitman, London-San Francisco-Melbourne, 1979, xvii + 369 pp., $46.00.
Maurice Auslander, On regular group rings, Proc. Amer. Math. Soc. 8 (1957), 658–664. MR 87670, DOI 10.1090/S0002-9939-1957-0087670-X
Victor P. Camillo, Semihereditary polynomial rings, Proc. Amer. Math. Soc. 45 (1974), 173–174. MR 352165, DOI 10.1090/S0002-9939-1974-0352165-2
Peter Gabriel and Ulrich Oberst, Spektralkategorien und reguläre Ringe im von-Neumannschen Sinn, Math. Z. 92 (1966), 389–395 (German). MR 225848, DOI 10.1007/BF01112218
Manabu Harada, Note on the dimension of modules and algebras, J. Inst. Polytech. Osaka City Univ. Ser. A 7 (1956), 17–27. MR 81269
Nathan Jacobson, Structure of rings, Revised edition, American Mathematical Society Colloquium Publications, Vol. 37, American Mathematical Society, Providence, R.I., 1964. MR 0222106
R. E. Johnson, The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891–895. MR 45695, DOI 10.1090/S0002-9939-1951-0045695-9
R. E. Johnson and E. T. Wong, Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260–268. MR 131445, DOI 10.1112/jlms/s1-36.1.260
Irving Kaplansky, Rings of operators, W. A. Benjamin, Inc., New York-Amsterdam, 1968. MR 0244778
P. J. McCarthy, The ring of polynomial over a von Neumann regular ring, Proc. Amer. Math. Soc. 39 (1973), 253–254. MR 316496, DOI 10.1090/S0002-9939-1973-0316496-3
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
R. S. Pierce, Modules over commutative regular rings, Memoirs of the American Mathematical Society, No. 70, American Mathematical Society, Providence, R.I., 1967. MR 0217056
Jan-Erik Roos, Sur l’anneau maximal de fractions des $AW^*$-algèbres et des anneaux de Baer, C. R. Acad. Sci. Paris Sér. A-B 266 (1968), A120–A123 (French). MR 244779
Alex Rosenberg and Daniel Zelinsky, Finiteness of the injective hull, Math. Z. 70 (1958/59), 372–380. MR 105434, DOI 10.1007/BF01558598
14. J. von Neumann, On regular rings, Proc. Nat Acad. Sci. U.S.A. 22 (1936), 707-713.
- 1.
- M. Auslander, On regular group rings, Proc. Amer. Math. Soc. 8 (1957), 658-664. MR 0087670
- 2.
- V. Camillo, Semihereditary polynomial rings, Proc. Amer. Math. Soc. 45 (1974), 173-174. MR 352165
- 3.
- P. Gabriel and U. Oberst, Spektralkategorien und regulare Ringe im Von-Neumannschen Sinn, Math. Z. 92 (1964), 389-395. MR 225848
- 4.
- M. Harada, Note on the dimension of modules and algebras, J. Inst. Poly. Osaka City Univ. 7 (1956), 17-27. MR 81269
- 5.
- N. Jacobson, Structure of rings, (2nd ed.), Amer. Math. Soc. Colloq. Publ., no. 37, Amer. Math. Soc., Providence, R. I., 1964. MR 222106
- 6.
- R. E. Johnson, The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895. MR 45695
- 7.
- R. E. Johnson and E. T. Wong, Quasi-injective modules and irreducible rings, J. London Math. Soc. 36 (1961), 260-268. MR 131445
- 8.
- I. Kaplansky, Rings of operators, Benjamin, New York, 1968. MR 244778
- 9.
- P. J. McCarthy, The ring of polynomials over a von Neumann regular ring, Proc. Amer. Math. Soc. 39 (1973), 253-254. MR 316496
- 10.
- F. J. Murray and J. von Neumann, On rings of operators, Ann. of Math. 37 (1936), 116-229. MR 1503275
- 11.
- R. S. Pierce, Modules over commutative regular rings, Mem. Amer. Math. Soc. No. 70 (1967). MR 217056
- 12.
- J.-E. Roos, Sur l'anneau maximal des fractions des AW*-algebras, C. R. Acad. Sci. Paris Ser. A-B 266 (1968), 120-123. MR 244779
- 13.
- A. Rosenberg and D. Zelinsky, Finiteness of the infective hull, Math. Z. 70 (1959), 372-380. MR 105434
- 14.
- J. von Neumann, On regular rings, Proc. Nat Acad. Sci. U.S.A. 22 (1936), 707-713.
Review Information:
Reviewer:
Efraim P. Armendariz
Journal:
Bull. Amer. Math. Soc.
3 (1980), 752-757
DOI:
https://doi.org/10.1090/S0273-0979-1980-14812-0
