A categorical contribution to the Kummer theory of ideal numbers

Ladislav Skula

Mathematica Slovaca (2003)

  • Volume: 53, Issue: 3, page 255-271
  • ISSN: 0139-9918

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Skula, Ladislav. "A categorical contribution to the Kummer theory of ideal numbers." Mathematica Slovaca 53.3 (2003): 255-271. <http://eudml.org/doc/31687>.

@article{Skula2003,
author = {Skula, Ladislav},
journal = {Mathematica Slovaca},
keywords = {Kummer's ideal complex numbers; theory of divisors; Čech-Stone -compactification; reflective subcategory; reflection},
language = {eng},
number = {3},
pages = {255-271},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {A categorical contribution to the Kummer theory of ideal numbers},
url = {http://eudml.org/doc/31687},
volume = {53},
year = {2003},
}

TY - JOUR
AU - Skula, Ladislav
TI - A categorical contribution to the Kummer theory of ideal numbers
JO - Mathematica Slovaca
PY - 2003
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 53
IS - 3
SP - 255
EP - 271
LA - eng
KW - Kummer's ideal complex numbers; theory of divisors; Čech-Stone -compactification; reflective subcategory; reflection
UR - http://eudml.org/doc/31687
ER -

References

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  1. ARNOLD I., Ideale in kommutativen Halbgruppen, Recueil Math. Moscow 36 (1929), 401-407. (1929) 
  2. BOREVICH Z. L.-SHAFARVICH I. R., Number Theory, Academic Press, Inc, Orlando, 1966 [Translation from Russian (1964)]. (1966) Zbl0145.04902MR0195803
  3. CLIFFORD A. H., Arithemtic and ideal theory of abstract multiplication, Bull. Amer. Math. Soc. 15 (1934), 326-330. (1934) MR1562845
  4. CLIFFORD A. H., Arithmetic and ideal theory of commutative semigroups, Ann. of Math. (2) 39 (1938), 594-610. (1938) Zbl0019.19401MR1503427
  5. HERRLICH H., Topologische Reflexionen und Coreflexionen, Lectures Notes in Math. 78, Springer-Verlag, Berlin-Heidelberg-New York, 1968. (1968) Zbl0182.25302MR0256332
  6. HERRLICH H.-STRECKER G. E., Category Theory, Allyn and Bacon, Boston, 1973. (1973) Zbl0265.18001MR0349791
  7. KUMMER E. E., Zur Theorie der komplexen Zahlen, Berlin. Monatsber. (1845), 87-96 (Abgedruckt in: J. Reine Angew. Math. 35 (1847), 319-326. Collected Papers, 203-210). 
  8. KUMMER E. E., Über die Zerlegung der aus Wurzeln der Einheit gebildeten komplexen Zahlen in ihre Primfactoren, J. Reine Angew. Math. 35 (1847), 327-367 (Collected Papers, 211-251). 
  9. MITCHELL B., Theory of Categories, Academic Press, New York and London, 1965. (1965) Zbl0136.00604MR0202787
  10. POSPÍŠIL B., Remark on bicompact spaces, Ann. of Math. (2) 38 (1937), 845-846. (1937) Zbl0017.42901MR1503375
  11. RIBENBOIM P., The work of Kummer on Fermaťs last theorem, In: Proc. Conf., Prog. Math. 26 (1982), pp. 1-29. (1982) MR0685285
  12. SKULA L., Divisorentheorie einer Halbgruppe, Math. Z. 114 (1970), 113-120. (1970) Zbl0177.03202MR0262401
  13. SKULA L., Fortsetzung stetiger Homomorphismen von δ -Halbgruppen, J. Reine Angew. Math. 261 (1973), 71-87. (1973) Zbl0266.20067MR0342633
  14. SKULA L., Maximale δ - und δ 1 -Kategorien, J. Reine Angew. Math. 274/275 (1975), 287-298. (1975) Zbl0308.20048MR0393199
  15. WALKER R. C., The Stone-Čech Compactification, Springer-Verlag, Berlin-Heidelberg-New York, 1974. (1974) Zbl0292.54001MR0380698

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