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Normal domains with monomial presentations

Journal Contribution - Journal Article

Let $A$ be a finitely generated commutative algebra
over a field $K$ with a presentation $A= K\langle
X_{1},\ldots ,X_{n} \mid R\rangle$, where $R$ is a
set of monomial relations in the generators
$X_{1},\ldots , X_{n}$. So $A=K[S]$, the semigroup
algebra of the monoid $S=\langle X_{1},\ldots ,X_{n}
\mid R\rangle$. We characterize, purely in terms of
the defining relations, when $A$ is an integrally
closed domain, provided $R$ contains at most two
relations. Also the class group of such algebras $A$
is calculated.
Journal: International Journal of Algebra & Computation
ISSN: 0218-1967
Issue: 3
Volume: 19
Pages: 287-303
Publication year:2009
Keywords:normal domain, class group, finitely presented algebra, semigroup algebra, commutative semigroup
  • Scopus Id: 66249094519
  • ORCID: /0000-0002-2695-7949/work/70477272