On Serre dimension of monoid algebras and Segre extensions |
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Affiliation: | 1. Université catholique de Louvain, Institut de Recherche en Mathématique et Physique, 1348 Louvain-la-Neuve, Belgium;2. Università degli Studi di Padova, Dipartimento di Matematica “Tullio Levi-Civita”, 35121 Padova, Italy;1. Department of Mathematics, Endenicher Allee 60, 53115 Bonn, Germany;2. Department of Mathematics, 1650 Bedford Avenue, 11225 Brooklyn, United States;3. Mathematics Program, The Graduate Center, CUNY, 365 Fifth Avenue, 10016 New York, United States;1. School of Mathematical Sciences & Academy for Multidisciplinary Studies, Capital Normal University, 100048 Beijing, China;2. School of Mathematical Sciences, Capital Normal University, 100048 Beijing, China;3. Department of Mathematics, Uppsala University, Box 480, 75106 Uppsala, Sweden |
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Abstract: | Let R be a commutative noetherian ring of dimension d and M be a commutative, cancellative, torsion-free monoid of rank r. Then S-. Further, we define a class of monoids such that if is seminormal, then S-, where . As an application, we prove that for the Segre extension over R, S-. |
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Keywords: | Unimodular elements Serre dimension Serre splitting Monoid algebra Segre extension Monic inversion |
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