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ArticleOriginal scientific text

Title

A structure theorem for sets of lengths

Authors 1

Affiliations

  1. Institut für Mathematik, Karl-Franzens-Universität, Heinrichstraße 36 8010 Graz, Austria

Bibliography

  1. [An] D. D. Anderson (ed.), Factorization in Integral Domains, Lecture Notes in Pure and Appl. Math. 189, Marcel Dekker, 1997.
  2. [A-M-Z] D. D. Anderson, J. L. Mott and M. Zafrullah, Finite character representations for integral domains, Boll. Un. Mat. Ital. B (7) 6 (1992), 613-630.
  3. [Bo] N. Bourbaki, Commutative Algebra, Springer, 1989.
  4. [Cha-Ge] S. Chapman and A. Geroldinger, Krull domains and monoids, their sets of lengths and associated combinatorial problems, in: [An], 73-112.
  5. [Ge1] A. Geroldinger, Über nicht-eindeutige Zerlegungen in irreduzible Elemente, Math. Z. 197 (1988), 505-529.
  6. [Ge2] A. Geroldinger, Chains of factorizations in weakly Krull domains, Colloq. Math. 72 (1997), 53-81.
  7. [Ge3] A. Geroldinger, Chains of factorizations and sets of lengths, J. Algebra 188 (1997), 331-362.
  8. [Ge4] A. Geroldinger, The catenary degree and tameness of factorizations in weakly Krull domains, in: [An], 113-153.
  9. [Ge5] A. Geroldinger, On the structure and arithmetic of finitely primary monoids, Czechoslovak Math. J. 46 (1996), 677-695.
  10. [Ge6] A. Geroldinger, T-block monoids and their arithmetical applications to certain integral domains, Comm. Algebra 22 (1994), 1603-1615.
  11. [G-L] A. Geroldinger and G. Lettl, Factorization problems in semigroups, Semigroup Forum 40 (1990), 23-38.
  12. [Gi] R. Gilmer, Commutative Semigroup Rings, The University of Chicago Press, 1984.
  13. [HK1] F. Halter-Koch, Über Längen nicht-eindeutiger Faktorisierungen und Systeme linearer diophantischer Ungleichungen, Abh. Math. Sem. Univ. Hamburg 63 (1993), 265 -276.
  14. [HK2] F. Halter-Koch, Finitely generated monoids, finitely primary monoids and factorization properties of integral domains, in: [An], 31-72.
  15. [HK3] F. Halter-Koch, The integral closure of a finitely generated monoid and the Frobenius problem in higher dimensions, in: Semigroups, C. Bonzini, A. Cherubini and C. Tibiletti (eds.), World Scientific, 1993, 86-93.
  16. [HK4] F. Halter-Koch, Finiteness theorems for factorizations, Semigroup Forum 44 (1992), 112-117.
  17. [HK5] F. Halter-Koch, Divisor theories with primary elements and weakly Krull domains, Boll. Un. Mat. Ital. B (7) 9 (1995), 417-441.
  18. [HK6] F. Halter-Koch, Elasticity of factorizations in atomic monoids and integral domains, J. Théor. Nombres Bordeaux 7 (1995), 367-385.
  19. [Ka] F. Kainrath, Factorization in Krull monoids with infinite class group.
  20. [Na1] W. Narkiewicz, Finite abelian groups and factorization problems, Colloq. Math. 42 (1979), 319-330.
  21. [Sc] H. Scheid, Zahlentheorie, 2. Auflage, B.I. Wissenschaftsverlag, 1994.
  22. [Sl] J. Śliwa, Remarks on factorizations in algebraic number fields, Colloq. Math. 46 (1982), 123-130.
  23. [Wa] L. C. Washington, Introduction to Cyclotomic Fields, 2nd ed., Springer, 1997.
Colloquium Mathematicum
1998/78/2
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Pages:
225-259
Main language of publication
English
Received
1997-08-20
Accepted
1998-03-20
Published
1998
Exact and natural sciences