• Title/Summary/Keyword: seminormal

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GENERALIZED NORMALITY IN RING EXTENSIONS INVOLVING AMALGAMATED ALGEBRAS

  • Kwon, Tae In;Kim, Hwankoo
    • Korean Journal of Mathematics
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    • v.26 no.4
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    • pp.701-708
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    • 2018
  • In this paper, seminormality and t-closedness in ring extensions involving amalgamated algebras are studied. Let $R{\subseteq}T$ be a ring extension with ideals $I{\subseteq}J$, respectively such that J is contained in the conductor of R in T. Assume that T is integral over R. Then it is shown that ($R{\bowtie}I$, $T{\bowtie}J$) is a seminormal (resp., t-closed) pair if and only if (R, T) is a seminormal (resp., t-closed) pair.

NOTES ON GRADING MONOIDS

  • Lee, Je-Yoon;Park, Chul-Hwan
    • East Asian mathematical journal
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    • v.22 no.2
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    • pp.189-194
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    • 2006
  • Throughout this paper, a semigroup S will denote a torsion free grading monoid, and it is a non-zero semigroup with 0. The operation is written additively. The aim of this paper is to study semigroup version of an integral domain ([1],[3],[4] and [5]).

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PROPERTIES OF HURWITZ POLYNOMIAL AND HURWITZ SERIES RINGS

  • Elliott, Jesse;Kim, Hwankoo
    • Bulletin of the Korean Mathematical Society
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    • v.55 no.3
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    • pp.837-849
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    • 2018
  • In this paper, we study the closedness such as seminomality and t-closedness, and Noetherian-like properties such as piecewise Noetherianness and Noetherian spectrum, of Hurwitz polynomial rings and Hurwitz series rings. To do so, we construct an isomorphism between a Hurwitz polynomial ring (resp., a Hurwitz series ring) and a factor ring of a polynomial ring (resp., a power series ring) in a countably infinite number of indeterminates.