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Abstract
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Let
be an integral
domain and
be
a torsion-free commutative cancellative (additive) semigroup with identity element and quotient
group
. We
show that if
(resp.,
), then
is a weakly Krull domain if
and only if
is a weakly Krull
UMT-domain,
is a weakly
Krull UMT-monoid, and
is of type
(resp., type
except
).
Moreover, we give arithmetical applications of this result.
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Keywords
semigroup ring, weakly Krull domain, finite $t$-character,
system of sets of lengths
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Mathematical Subject Classification
Primary: 13A15, 13F05, 20M12
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Milestones
Received: 24 January 2022
Revised: 21 April 2022
Accepted: 21 May 2022
Published: 20 August 2022
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