JP Journal of Algebra, Number Theory and Applications
Volume 2, Issue 3, Pages 205 - 239
(December 2002)
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TAMELY GENERATED IDEALS IN
FINITARY MONOIDS
Alfred Geroldinger (Austria) and Franz Halter-Koch (Austria)
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Abstract: The Structure Theorem for Sets of Lengths is one
of the most important results in the theory of
non-unique factorizations. In this paper, we
investigate the theory of tamely generated and
of complete ideals in finitary monoids. These
ideals play the key role in the algebraic
background for the Structure Theorem for Sets of
Lengths, and the results of this paper make it
possible to prove that Theorem for congruence
monoids in Dedekind domains and for a large
class of finitely generated domains. Apart from
the arithmetical applications, the theory of
these ideals gives a good insight into the
structure of G-monoids and of monoids with only
finitely many prime ideals. |
Keywords and phrases: factorizations, sets of lengths, finitary monoids. |
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