The role of semigroups in the elementary theory of numbers

Štefan Schwarz

Mathematica Slovaca (1981)

  • Volume: 31, Issue: 4, page 369-395
  • ISSN: 0232-0525

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Schwarz, Štefan. "The role of semigroups in the elementary theory of numbers." Mathematica Slovaca 31.4 (1981): 369-395. <http://eudml.org/doc/31641>.

@article{Schwarz1981,
author = {Schwarz, Štefan},
journal = {Mathematica Slovaca},
keywords = {Euler-Fermat theorem; Wilson theorem; multiplicative semigroup; idempotents},
language = {eng},
number = {4},
pages = {369-395},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {The role of semigroups in the elementary theory of numbers},
url = {http://eudml.org/doc/31641},
volume = {31},
year = {1981},
}

TY - JOUR
AU - Schwarz, Štefan
TI - The role of semigroups in the elementary theory of numbers
JO - Mathematica Slovaca
PY - 1981
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 31
IS - 4
SP - 369
EP - 395
LA - eng
KW - Euler-Fermat theorem; Wilson theorem; multiplicative semigroup; idempotents
UR - http://eudml.org/doc/31641
ER -

References

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  1. CORDES C. M., Permutations mod m in the foгm xn, Amer. Math. Monthly 83, 1976, 32-33. (1976) MR0460222
  2. HEWITT E., ZUCKERMAN H. S., The multiplicative semigroup of integers (mod m), Pacific J. Math. 10, 1960, 1291-1308. (1960) MR0125892
  3. HEWITT E., Ceгtain congruences that hold identically, Amer. Math. Monthly 83, 1976, 270-271. (1976) MR0434933
  4. KOWOL G., MITSCH H., Polynomial functions over commutative semigгoups, Semigroup Forum 12, 1976, 109-118. (1976) MR0404501
  5. LIVINGSTON A. E., LIVINGSTON M. L., The congruence а r + s = a s ( m o d m ) , Ameг. Math. Monthy 85, 1978, 97-100. (1978) Zbl0375.10002MR0472660
  6. MORGADO J., A pгopeгty of the Euleг 𝜓 -function concerning the integers which are гegular (mod m), Poгtugal. Math. 33, 1974, 185-191. (1974) MR0419336
  7. OSBORN R., A "good" generalization of the Euleг-Fermat theorem, Math. Mag. 47, 1974, 28-31. (1974) MR0335415
  8. PARÍZEK B., SCHWARZ Š., O multiplikatívnej pologгupe zvyškových tried (mod m), Mat.-Fyz. Časop. 8, 1958, 136-150. (1958) MR0103938
  9. PARÍZEK B., O rozklade pologrupy zvyškov (mod m) na diгektný súčin, Mat.-Fyz. Časop. 10, 1960, 18-29. (1960) 
  10. SINGMASTER D., A maximal generalization of Feгmaťs theoгem, Math. Mag. 39, 1966, 103-107. (1966) MR0197386
  11. SMALL, CH., Powers mod m, Math. Mag. 50, 1977, 84-86. (1977) MR0437433
  12. VANDIVER H. S., WEAVER H. W., Intгoduction to arithmetic factorization and congгuences fгom the standpoint of abstгact algebгa, H. E. Slaught Memorial Papers, no. 7, 1958, Math. Assoc. of America. (1958) 
  13. ZANE B., Uniform distribution (mod m) of monomials, Ameг. Math. Monthly 71, 1964, 162-164. (1964) MR0161829
  14. BUCHŠTAB A. A., Teorija čisel, Gos. uč.-ped. izd., Moskva, 1960. (1960) 
  15. DICKSON L. E., BODEWIG E., Intгoduction to the Theoгy of Numbeгs, (German edition.) Teubneг, Leipzig, 1931. (1931) 

Citations in EuDML Documents

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  1. Štefan Schwarz, An unconventional problem in the elementary theory of numbers
  2. Otokar Grošek, Remarks concerning RSA-cryptosystem exponents
  3. Miroslav Lašák, Wilson's theorem in algebraic number fields
  4. Otokar Grošek, O vzťahu akademika Štefana Schwarza k aplikáciám matematiky
  5. Karol Nemoga, Štefan Schwarz, An explicit description of the set of all normal bases generators of a finite field
  6. Štefan Schwarz, Extensions of Bauer's identical congruences
  7. Alessandra Cherubini, Ada Varisco, On E k -rings
  8. Imrich Abrhan, О простых идеалах в группоидах и в мультипликативных полугруппах классов вычетов (mod m)
  9. Beloslav Riečan, Štefan Schwarz (1914–1996)
  10. Ján Jakubík, Milan Kolibiar, Eighty years of Professor Štefan Schwarz

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