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Systems Of Linear Congruences

Published online by Cambridge University Press:  20 November 2018

A. T. Butson  and
B. M. Stewart
A. T. Butson
Affiliation:
Michigan State College
B. M. Stewart
Affiliation:
Michigan State College
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1. Introduction. On recent occasions papers have been presented concerned with the problem of solving a system of linear congruences. Apparently the authors were not aware that this problem was solved very neatly and completely a long time ago by H. J. S. Smith (5; 6).

Type
Research Article
Information
Canadian Journal of Mathematics , Volume 7 , 1955 , pp. 358 - 368
Copyright
Copyright © Canadian Mathematical Society 1955

References

1. Dickson, L. E., Algebras and their arithmetics, (Chicago, 1923).Google Scholar
2. MacDuffee, C. C., An introduction to the theory of ideals in linear associative algebras. Trans. Amer. Math. Soc, 31 (1929), 71–90.Google Scholar
3. MacDuffee, C. C., Modules and ideals in a Frobenius algebra, Monatsh. Math., 48 (1939), 293–313.Google Scholar
4. MacDuffee, C. C., An introduction to abstract algebra (New York, 1940).Google Scholar
5. Smith, H. J. S., On systems of linear indeterminate equations and congruences, Phil. Trans. Royal Soc. London, A 151 (1861), 293–326.Google Scholar
6. Smith, H. J. S., On the arithmetical invariants of a rectangular matrix of which the constituents are integral numbers, Proc. London Math. Soc, 4 (1873), 236–249.Google Scholar
7. Stewart, B. M., A note on least common left multiples, Bull. Amer. Math. Soc, 55 (1949), 587–591.Google Scholar
8. Stieltjes, T. J., Oeuvres complètes, II (Math. Soc. Amsterdam, 1918).Google Scholar
9. Sylvester, J. J., C.R. Acad. Sci., Paris, 99 (1884), 117–118, 409–412, 432–436, 527–529.Google Scholar