• Bulletin of the Korean Mathematical Society
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• v.52 no.2
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• pp.525-530
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• 2015

Let D be an integrally closed domain with quotient field K, X be an indeterminate over D, $f=a_0+a_1X+{\cdots}+a_nX^n{\in}D[X]$ be irreducible in K[X], and $Q_f=fK[X]{\cap}D[X]$. In this paper, we show that $Q_f$ is a maximal ideal of D[X] if and only if $(\frac{a_1}{a_0},{\cdots},\frac{a_n}{a_0}){\subseteq}P$ for all nonzero prime ideals P of D; in this case, $Q_f=\frac{1}{a_0}fD[X]$. As a corollary, we have that if D is a Krull domain, then D has infinitely many height-one prime ideals if and only if each maximal ideal of D[X] has height ${\geq}2$.

• Communications of the Korean Mathematical Society
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• v.22 no.4
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• pp.503-508
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• 2007

Using the notion of posets, a method to make BCK-algebras is considered. We show that if a poset has the least element, then the induced BCK-algebra is bounded.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.1-5
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• 2010

Let P be a prime ideal of a commutative unital ring R; X an indeterminate; D := R/P; L the quotient field of D; F an algebraic closure of L; ${\alpha}$ ${\in}$ L[X] a monic irreducible polynomial; ${\xi}$ any root of in F; and Q = ${\alpha}$>, the upper to P with respect to ${\alpha}$. Then R[X]/Q is R-algebra isomorphic to $D[{\xi}]$; and is R-isomorphic to an overring of D if and only if deg(${\alpha}$) = 1.

• Communications of the Korean Mathematical Society
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• v.21 no.4
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• pp.641-652
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• 2006

In [2], they found some natural generators for the ideals of the finite ring $Z_{pm}$[X]/$(X^n\;-\;1)$, where p and n are relatively prime. If p and n are not relatively prime $X^n\;-\;1$ is not a product of basic irreducible polynomials but a product of primary polynomials. Due to this fact, to consider the ideals of $Z_{pm}$[X]/$(X^n\;-\;1)$ in 'inseparable' case we need to look at the primary ideals of $Z_{pm}$[X]. In this paper, we find a set of generators of ideals of $Z_{pm}$[X]/(f) for some primary polynomials f of $Z_{pm}$[X].

• Bulletin of the Korean Mathematical Society
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• v.45 no.3
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• pp.457-466
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• 2008

Let R be a right near-ring. An R-group of type-5/2 which is a natural generalization of an irreducible (ring) module is introduced in near-rings. An R-group of type-5/2 is an R-group of type-2 and an R-group of type-3 is an R-group of type-5/2. Using it $J_{5/2}$, the Jacobson radical of type-5/2, is introduced in near-rings and it is observed that $J_2(R){\subseteq}J_{5/2}(R){\subseteq}J_3(R)$. It is shown that $J_{5/2}$ is an ideal-hereditary Kurosh-Amitsur radical (KA-radical) in the class of all zero-symmetric near-rings. But $J_{5/2}$ is not a KA-radical in the class of all near-rings. By introducing an R-group of type-(5/2)(0) it is shown that $J_{(5/2)(0)}$, the corresponding Jacobson radical of type-(5/2)(0), is a KA-radical in the class of all near-rings which extends the radical $J_{5/2}$ of zero-symmetric near-rings to the class of all near-rings.