Bulletin of the American Mathematical Society

MathSciNet review: 1566972
Full text of review: PDF   This review is available free of charge.
Book Information:

Author: Bo Stenström
Title: Rings of quotients
Additional book information: Die Grundlehren der mathematischen Wissenschaften in Einzeldarstellungen, Band 217, Springer-Verlag, New York, Heidelberg, Berlin, 1975, viii + 309 pp., $39.60.

Keizo Asano, Über die Quotientenbildung von Schiefringen, J. Math. Soc. Japan 1 (1949), 73–78 (German). MR 31468, DOI 10.2969/jmsj/00120073

A. W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3) 8 (1958), 589–608. MR 103206, DOI 10.1112/plms/s3-8.4.589

A. W. Goldie, Semi-prime rings with maximum condition, Proc. London Math. Soc. (3) 10 (1960), 201–220. MR 111766, DOI 10.1112/plms/s3-10.1.201

Nathan Jacobson, The Theory of Rings, American Mathematical Society Mathematical Surveys, Vol. II, American Mathematical Society, New York, 1943. MR 0008601

Arun Vinayak Jategaonkar, Relative Krull dimension and prime ideals in right Noetherian rings, Comm. Algebra 2 (1974), 429–468. MR 357494, DOI 10.1080/00927877408822020

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

Wallace S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576–584. MR 238897, DOI 10.1016/0021-8693(69)90029-5

Oystein Ore, Linear equations in non-commutative fields, Ann. of Math. (2) 32 (1931), no. 3, 463–477. MR 1503010, DOI 10.2307/1968245

Yuzo Utumi, On quotient rings, Osaka Math. J. 8 (1956), 1–18. MR 78966

A. I. Uzkov, On rings of quotients of commutative rings, Mat. Sbornik N. S. 22(64) (1948), 439–441 (Russian). MR 0026041

1.

K. Asano, Über die Quotientenbildung von Schiefringen, J. Math. Soc. Japan 1 (1949), 73-78. MR 11, 154. MR 0031468

2.

A. W. Goldie, The structure of prime rings under ascending chain conditions, Proc. London Math. Soc. (3) 8 (1958), 589-608. MR 21 # 1988. MR 103206

3.

A. W. Goldie, Semi-prime rings with maximum conditions, Proc. London Math. Soc. (3) 10 (1960), 201-220. MR 22 #2627. MR 111766

4.

N. Jacobson, The theory of rings, Math. Surveys, vol. 2, Amer. Math. Soc. Providence, R.I., 1943. MR 5, 31. MR 8601

5.

A. V. Jategaonkar, Relative Krull dimension and prime ideals in right Noetherian rings9 Comm. Algebra 2 (1974), 429-468. MR 50 #9962. MR 357494

6.

R. E. Johnson, The extended centralizer of a ring over a module, Proc. Amer. Math. Soc. 2 (1951), 891-895. MR 13, 618. MR 45695

7.

W. S. Martindale III, Prime rings satisfying a generalized polynomial identity, J. Algebra 12 (1969), 576-584. MR 39 #257. MR 238897

8.

O. Ore, Linear equations in non-commutative fields, Ann. of Math. (2) 32 (1931), 463-477. MR 1503010

9.

Y. Utumi, On quotient rings, Osaka Math. J. 8 (1956), 1-18. MR 18, 7. MR 78966

10.

A. I. Uzkov, On the rings of quotients of commutative rings, Mat. Sb. NS 22 (64) (1948), 439-441; English transl., Amer. Math. Soc. Transl. (1) 1 (1962), 470-473. MR 10, 97. MR 26041