• Bulletin of the Korean Mathematical Society
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• v.44 no.4
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• pp.771-775
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• 2007

In this note we discussed the half-factoriality of Krull monoid domain D[S] whenever the monoid S has trivial divisor class group.

• Bulletin of the Korean Mathematical Society
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• v.59 no.2
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• pp.361-373
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• 2022

We study the factoriality of a nodal quartic hypersurface V₄ in ℙ⁴ when there is a hyperplane in ℙ⁴ containing all the nodes of V₄. As an application, we obtain new examples of irrational quartic 3-folds.

• The Pure and Applied Mathematics
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• v.29 no.2
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• pp.201-206
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• 2022

Let X be a nodal complete intersection 3-fold defined by a hypersurface in ℙ⁵ of degree n and a smooth quadratic hypersurface in ℙ⁵ . Then we show that X is factorial if it has at most n² - n + 1 nodes and contains no 2-planes, where n = 3, 4.

• Communications of the Korean Mathematical Society
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• v.39 no.2
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• pp.313-329
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• 2024

An (additive) commutative monoid is called atomic if every given non-invertible element can be written as a sum of atoms (i.e., irreducible elements), in which case, such a sum is called a factorization of the given element. The number of atoms (counting repetitions) in the corresponding sum is called the length of the factorization. Following Geroldinger and Zhong, we say that an atomic monoid M is a length-finite factorization monoid if each b ∈ M has only finitely many factorizations of any prescribed length. An additive submonoid of ℝ_≥0 is called a positive monoid. Factorizations in positive monoids have been actively studied in recent years. The main purpose of this paper is to give a better understanding of the non-unique factorization phenomenon in positive monoids through the lens of the length-finite factorization property. To do so, we identify a large class of positive monoids which satisfy the length-finite factorization property. Then we compare the length-finite factorization property to the bounded and the finite factorization properties, which are two properties that have been systematically investigated for more than thirty years.