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Abstract
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(1) Let
be a commutative Noetherian ring of dimension
and
a
commutative partially cancellative torsion-free seminormal monoid. Then
is injective
stable at
.
This settles a conjecture of Gubeladze for the mentioned class of monoids.
(2) Take the same
as in (1) with an additional assumption that
has a positive characteristic
which is prime to
.
Let
be a
commutative cancellative torsion-free seminormal positive monoid with a radical ideal
. Then
the map
is
surjective for
.
This answers a question of Wiemers in some special cases.
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Keywords
algebraic $K$-theory, $K_0$-stability, projective module,
projective cancellation, partially cancellative monoids,
monoid algebra
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Mathematical Subject Classification 2010
Primary: 19A13
Secondary: 13C10, 13D15
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Milestones
Received: 1 January 2020
Revised: 4 April 2021
Accepted: 22 April 2021
Published: 12 February 2022
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