Elasticity of factorizations in atomic monoids and integral domains

Franz Halter-Koch

Journal de théorie des nombres de Bordeaux (1995)

  • Volume: 7, Issue: 2, page 367-385
  • ISSN: 1246-7405

Abstract

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For an atomic domain R , its elasticity ρ ( R ) is defined by : ρ ( R ) = sup { m / n u 1 ⋯ u m = v 1 ⋯ v n for irreducible u j , v i ∈ R } . We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants μ m ( R ) defined by : μ m ( R ) = sup { n u 1 ⋯ u m = u 1 ⋯ v n for irreducible u j , v i ∈ R } . As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants μ m and ρ for monoids and integral domains which are of independent interest.

How to cite

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Halter-Koch, Franz. "Elasticity of factorizations in atomic monoids and integral domains." Journal de théorie des nombres de Bordeaux 7.2 (1995): 367-385. <http://eudml.org/doc/247668>.

@article{Halter1995,
abstract = {For an atomic domain $R$, its elasticity $\rho (R)$ is defined by : $\rho (R) = \sup \lbrace m/n \left| u_1 \cdots u_m = v_1 \cdots v_n\right.$ for irreducible $u_j, v_i \in R \rbrace $. We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants $\mu _m (R)$ defined by : $\mu _m(R) = \sup \lbrace n\left|u_1 \cdots u_m = u_1 \cdots v_n\right.$ for irreducible $u_j, v_i \in R \rbrace $. As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants $\mu _m$ and $\rho $ for monoids and integral domains which are of independent interest.},
author = {Halter-Koch, Franz},
journal = {Journal de théorie des nombres de Bordeaux},
keywords = {length of factorization; orders with finite elasticity; elasticity; atomic integral domain; atomic monoids; Krull domain; divisor class group},
language = {eng},
number = {2},
pages = {367-385},
publisher = {Université Bordeaux I},
title = {Elasticity of factorizations in atomic monoids and integral domains},
url = {http://eudml.org/doc/247668},
volume = {7},
year = {1995},
}

TY - JOUR
AU - Halter-Koch, Franz
TI - Elasticity of factorizations in atomic monoids and integral domains
JO - Journal de théorie des nombres de Bordeaux
PY - 1995
PB - Université Bordeaux I
VL - 7
IS - 2
SP - 367
EP - 385
AB - For an atomic domain $R$, its elasticity $\rho (R)$ is defined by : $\rho (R) = \sup \lbrace m/n \left| u_1 \cdots u_m = v_1 \cdots v_n\right.$ for irreducible $u_j, v_i \in R \rbrace $. We study the elasticity of one-dimensional noetherian domains by means of the more subtle invariants $\mu _m (R)$ defined by : $\mu _m(R) = \sup \lbrace n\left|u_1 \cdots u_m = u_1 \cdots v_n\right.$ for irreducible $u_j, v_i \in R \rbrace $. As a main result we characterize all orders in algebraic number fields having finite elasticity. On the way, we obtain a series of results concerning the invariants $\mu _m$ and $\rho $ for monoids and integral domains which are of independent interest.
LA - eng
KW - length of factorization; orders with finite elasticity; elasticity; atomic integral domain; atomic monoids; Krull domain; divisor class group
UR - http://eudml.org/doc/247668
ER -

References

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Citations in EuDML Documents

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  1. Paul Baginski, Scott T. Chapman, George J. Schaeffer, On the Delta set of a singular arithmetical congruence monoid
  2. SooAh Chang, Scott T. Chapman, William W. Smith, Elasticity in certain block monoids via the Euclidean table
  3. Alfred Geroldinger, Chains of factorizations in weakly Krull domains
  4. Alfred Geroldinger, A structure theorem for sets of lengths
  5. Wolfgang A. Schmid, Differences in sets of lengths of Krull monoids with finite class group
  6. Alfred Geroldinger, On the structure and arithmetic of finitely primary monoids

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