Non-unique factorizations in block semigroups and arithmetical applications

Alfred Geroldinger; Franz Halter-Koch

Mathematica Slovaca (1992)

  • Volume: 42, Issue: 5, page 641-661
  • ISSN: 0139-9918

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Geroldinger, Alfred, and Halter-Koch, Franz. "Non-unique factorizations in block semigroups and arithmetical applications." Mathematica Slovaca 42.5 (1992): 641-661. <http://eudml.org/doc/31537>.

@article{Geroldinger1992,
author = {Geroldinger, Alfred, Halter-Koch, Franz},
journal = {Mathematica Slovaca},
keywords = {block semigroups; factorization; asymptotic behaviour; counting function of principal ideals},
language = {eng},
number = {5},
pages = {641-661},
publisher = {Mathematical Institute of the Slovak Academy of Sciences},
title = {Non-unique factorizations in block semigroups and arithmetical applications},
url = {http://eudml.org/doc/31537},
volume = {42},
year = {1992},
}

TY - JOUR
AU - Geroldinger, Alfred
AU - Halter-Koch, Franz
TI - Non-unique factorizations in block semigroups and arithmetical applications
JO - Mathematica Slovaca
PY - 1992
PB - Mathematical Institute of the Slovak Academy of Sciences
VL - 42
IS - 5
SP - 641
EP - 661
LA - eng
KW - block semigroups; factorization; asymptotic behaviour; counting function of principal ideals
UR - http://eudml.org/doc/31537
ER -

References

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  1. CARLITZ L., A characterization of algebraic number fields with class number two, Proc. Amer. Math. Soc. 11 (1960), 391-392. (1960) Zbl0202.33101MR0111741
  2. FUCHS L., Infinite Abelian Groups, Academic Press, Address of publisher, 1970. (1970) Zbl0209.05503MR0255673
  3. GEROLDINGER A., Über nicht-eindeutige Zerlegungen in irreduzible Elemente, Math. Z. 197 (1988), 505-529. (197) MR0932683
  4. GEROLDINGER A., Ein quantitatives Resultat über Faktorisierungen verschiedener Länge in algebraischen Zahlkörpern, Math. Z. 205 (1990), 159-162. (1990) Zbl0721.11041MR1069491
  5. GEROLDINGER A., Factorization of natural numbers in algebraic number fields, Acta Arith. 57 (1991), 365-373. (1991) Zbl0729.11054MR1109993
  6. GEROLDINGER A., HALTER-KOCH F., Realization Theorems for semigroups with divisor theory, Semigroup Forum 44 (1992), 229-237. (1992) Zbl0751.20045MR1141841
  7. HALTER-KOCH F., Halbgruppen mit Divisorentheorie, Exposition. Math. 8 (1990), 27-66. (1990) Zbl0698.20054MR1042201
  8. HALTER-KOCH F., A generalization of Davenport's constant and its arithmetical applications, Colloq. Math. 63 (1992), 203-210. (1992) Zbl0760.11031MR1180633
  9. HALTER-KOCH F., Typenhalbgruppen und Faktorisierungsprobleme, Resultate Math. 22 (1992), 545-559. (1992) Zbl0769.11039MR1174924
  10. HALTER-KOCH F., MÜLLER W., Quantitative aspects of non-unique factorization: A general theory with applications to algebraic function fields, J. Heine Angew. Math. 421 (1991), 159-188. (1991) Zbl0736.11064MR1129580
  11. KACZOROWSKI J., Some remarks on factorization in algebraic number fields, Acta Arith. 43 (1983), 53-68. (1983) Zbl0526.12006MR0730848
  12. NARKIEWICZ W., Finite abelian groups and factorization problems, Colloq. Math. 42 (1979), 319-330. (1979) Zbl0514.12004MR0567570
  13. NARKIEWICZ W., Elementary and Analytic Theory of Algebraic Numbers, Springer, Address of Publisher, 1990. (1990) Zbl0717.11045MR1055830
  14. NARKIEWICZ W., Numbers with unique factorization in an algebraic number field, Acta Arith. 21 (1972), 313-322. (1972) Zbl0215.07301MR0302611
  15. NARKIEWICZ W., SLIWA J., Finite abelian groups and factorization problems, II, Colloq. Math. 46 (1982), 115-122. (1982) Zbl1164.20358MR0672371
  16. SLIWA J., Factorizations of distinct lenghts in algebraic number fields, Acta Arith. 31 (1976), 399-417. (1976) MR0429830

Citations in EuDML Documents

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  1. Scott Chapman, William Smith, Finite cyclic groups and the k-HFD property
  2. SooAh Chang, Scott T. Chapman, William W. Smith, Elasticity in certain block monoids via the Euclidean table
  3. Wolfgang Alexander Schmid, Arithmetic of block monoids
  4. Franz Halter-Koch, Relative block semigroups and their arithmetical applications
  5. Wolfgang Alexander Schmid, On invariants related to non-unique factorizations in block monoids and rings of algebraic integers
  6. Franz Halter-Koch, Chebotarev formations and quantitative aspects of non-unique factorizations

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