Book Review
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MathSciNet review:
1567625
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Book Information:
Author:
J. D. P. Meldrum
Title:
Near-rings and their links with groups
Additional book information:
Pitman Publishing, Boston, London, Melbourne, 275 pp., $44.95. ISBN 0-470-20648-9.
Gerhard Betsch, Primitive near-rings, Math. Z. 130 (1973), 351–361. MR 325706, DOI 10.1007/BF01179162
Gerhard Betsch, Embedding of a near-ring into a near-ring with identity, Near-rings and near-fields (Tübingen, 1985) North-Holland Math. Stud., vol. 137, North-Holland, Amsterdam, 1987, pp. 37–40. MR 890754, DOI 10.1016/S0304-0208(08)72284-9
Bertram Huppert and Norman Blackburn, Finite groups. II, Grundlehren der Mathematischen Wissenschaften [Fundamental Principles of Mathematical Sciences], vol. 242, Springer-Verlag, Berlin-New York, 1982. AMD, 44. MR 650245
4. D. W. Blackett, Simple and semi-simple near-rings, doctoral dissertation, Princeton University, 1950.
P. Dembowski, Finite geometries, Ergebnisse der Mathematik und ihrer Grenzgebiete, Band 44, Springer-Verlag, Berlin-New York, 1968. MR 0233275
Leonard Eugene Dickson, Definitions of a group and a field by independent postulates, Trans. Amer. Math. Soc. 6 (1905), no. 2, 198–204. MR 1500706, DOI 10.1090/S0002-9947-1905-1500706-2
A. Fröhlich, Non-Abelian homological algebra. I. Derived functors and satellites, Proc. London Math. Soc. (3) 11 (1961), 239–275. MR 143794, DOI 10.1112/plms/s3-11.1.239
Marshall Hall Jr., The theory of groups, The Macmillan Company, New York, N.Y., 1959. MR 0103215
N. Jacobson, Representation theory for Jordan rings, Proceedings of the International Congress of Mathematicians, Cambridge, Mass., 1950, vol. 2, Amer. Math. Soc., Providence, R.I., 1952, pp. 37–43. MR 0044505
Helmut Karzel, Bericht über projektive Inzidenzgruppen, Jber. Deutsch. Math.-Verein. 67 (1964/65), no. Abt. 1, 58–92 (German). MR 175014
William Kerby, On infinite sharply multiply transitive groups, Hamburger Mathematische Einzelschriften (N.F.), Heft 6, Vandenhoeck & Ruprecht, Göttingen, 1974. MR 0384938
B. H. Neumann, On the commutativity of addition, J. London Math Soc. 15 (1940), 203–208. MR 0002851, DOI 10.1112/jlms/s1-15.3.203
Günter Pilz, Near-rings, 2nd ed., North-Holland Mathematics Studies, vol. 23, North-Holland Publishing Co., Amsterdam, 1983. The theory and its applications. MR 721171
Günter Pilz, What near-rings can do for you, Contributions to general algebra, 5 (Salzburg, 1986) Hölder-Pichler-Tempsky, Vienna, 1987, pp. 11–29. MR 930907
O. Veblen and J. H. Maclagan-Wedderburn, Non-Desarguesian and non-Pascalian geometries, Trans. Amer. Math. Soc. 8 (1907), no. 3, 379–388. MR 1500792, DOI 10.1090/S0002-9947-1907-1500792-1
Heinz Wähling, Theorie der Fastkörper, Thales Monographs, vol. 1, Thales-Verlag, Essen, 1987 (German). MR 956467
17. H. Wielandt, Über Bereiche aus Gruppenabbildungen, Deutsche Mathematik 3 (1938), 9-10.
18. H. Zassenhaus, Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg 11 (1935/36), 187-220.
J. L. Zemmer, The additive group of an infinite near-field is Abelian, J. London Math. Soc. 44 (1969), 65–67. MR 231902, DOI 10.1112/jlms/s1-44.1.65
- 1.
- G. Betsch, Primitive near-rings, Math. Z. 130 (1973), 351-361. MR 0325706
- 2.
- G. Betsch, (ed. ), Near-rings and near-fields, North-Holland, Amsterdam, 1987. MR 890754
- 3.
- N. Blackburn and B. Huppert, Finite groups. III, Springer, Berlin-Heidelberg-New York, 1982. MR 662826
- 4.
- D. W. Blackett, Simple and semi-simple near-rings, doctoral dissertation, Princeton University, 1950.
- 5.
- P. Dembrowski, Finite geometries, Springer, Berlin, 1968. MR 233275
- 6.
- L. E. Dickson, Definitions of a group and a field by independent postulates, Trans. Amer. Math. Soc. 6 (1905), 198-204. MR 1500706
- 7.
- A. Fröhlich, Non-abelian homological algebra. I, Derived functors and satellites, Proc. London Math. Soc. 11 (1961), 239-275. MR 143794
- 8.
- M. Hall, The theory of groups, McMillan, New York, 1959. MR 103215
- 9.
- N. Jacobson, Structure of rings, Amer. Math. Soc. Colloq. Publ., vol. 37, Providence, R. I., 1968. MR 44505
- 10.
- H. Karzel, Bericht über projektive Inzidenzgruppen, Jahresber. Dt. Math. Ver. 67 (1965), 58-92. MR 175014
- 11.
- W. E. Kerby, On infinite sharply multiply transitive groups, Vandenhoeck and Ruprecht, Göttingen, 1974. MR 384938
- 12.
- B. H. Neumann, On the commutativity of addition, J. London Math. Soc. 15 (1940), 203-208. MR 2851
- 13.
- G. Pilz, Near-rings, North-Holland, Amsterdam, second edition, 1983. MR 721171
- 14.
- G. Pilz, What near-rings can do for you, Contrib. to General Algebra 4, Teubner, Stuttgart, 1987. MR 930907
- 15.
- O. Veblen and J. H. Wedderburn, Non-desarguesian and non-pascalian geometries, Trans. Amer. Math. Soc. 8 (1907), 379-388. MR 1500792
- 16.
- H. Wähling, Theorie der Fastkörper, Thales Verlag, Essen, 1987. MR 956467
- 17.
- H. Wielandt, Über Bereiche aus Gruppenabbildungen, Deutsche Mathematik 3 (1938), 9-10.
- 18.
- H. Zassenhaus, Über endliche Fastkörper, Abh. Math. Sem. Univ. Hamburg 11 (1935/36), 187-220.
- 19.
- J. L. Zemmer, The additive group of an infinite near-field is abelian, J. London Math. Soc. 44 (1969), 65-67. MR 231902
Review Information:
Reviewer:
Günter F. Pilz
Journal:
Bull. Amer. Math. Soc.
17 (1987), 156-160
DOI:
https://doi.org/10.1090/S0273-0979-1987-15549-2
