• Communications of the Korean Mathematical Society
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• v.28 no.4
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• pp.669-677
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• 2013

In this paper we introduce the notion of NI near-rings similar to the notion introduced in rings. We give topological properties of collection of strongly prime ideals in NI near-rings. We have shown that if N is a NI and weakly pm near-ring, then $Max(N)$ is a compact Hausdorff space. We have also shown that if N is a NI near-ring, then for every $a{\in}N$, $cl(D(a))=V(N^*(N)_a)=Supp(a)=SSpec(N){\setminus}int\;V(a)$.

• Journal of the Korean Mathematical Society
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• v.47 no.2
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• pp.299-309
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• 2010

The Weyl group of a compact connected Lie group is a reflection group. If such Lie groups are locally isomorphic, the representations of the Weyl groups are rationally equivalent. They need not however be equivalent as integral representations. Turning to the invariant theory, the rational cohomology of a classifying space is a ring of invariants, which is a polynomial ring. In the modular case, we will ask if rings of invariants are polynomial algebras, and if each of them can be realized as the mod p cohomology of a space, particularly for dihedral groups.

• Bulletin of the Korean Mathematical Society
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• v.39 no.4
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• pp.645-652
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• 2002

In this note we investigate some results which concern the types of local rings. In particular it is shown that if the type of a quasi-unmixed local ring A is less than or equal to depth A ＋ 1, and $\hat{A}_p$ is Cohen-Macaulay for every prime $p\neq\hat{m}$, then A is Cohen-Macaulay. (This implies the previously known result: if A satisfies $(S_{n-1})}$, where n is the type of a .ins A, then A is Cohen-Macaulay.)

• 한국정보디스플레이학회:학술대회논문집
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• 2009.10a
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• pp.342-345
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• 2009

Bright light-emitting single crystal organic field-effect transistors (FETs) based on highly luminescent oligo(p-phenylenevinylene) (OPV) derivatives are demonstrated. Although OPV single crystal FETs show both p - and n - type FET operation, we found that an increase in the conjugation length of the OPV derivatives from three phenylene rings to five phenylene rings results in an improvement in the electron mobility by an order of magnitude, while retaining the high hole mobility with intense electroluminescence.

• Bulletin of the Korean Mathematical Society
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• v.58 no.4
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• pp.897-908
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• 2021

In this paper, we introduce the notion of pseudo 2-prime ideals in commutative rings. Let R be a commutative ring with a nonzero identity. A proper ideal P of R is said to be a pseudo 2-prime ideal if whenever xy ∈ P for some x, y ∈ R, then x²ⁿ ∈ Pⁿ or y²ⁿ ∈ Pⁿ for some n ∈ ℕ. Various examples and properties of pseudo 2-prime ideals are given. We also characterize pseudo 2-prime ideals of PID's and von Neumann regular rings. Finally, we use pseudo 2-prime ideals to characterize almost valuation domains (AV-domains).

• Journal of the Korean Mathematical Society
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• v.60 no.2
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• pp.327-339
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• 2023

Let R be a commutative ring with identity and S be a multiplicatively closed subset of R. In this article we introduce a new class of ring, called S-multiplication rings which are S-versions of multiplication rings. An R-module M is said to be S-multiplication if for each submodule N of M, sN ⊆ JM ⊆ N for some s ∈ S and ideal J of R (see for instance [4, Definition 1]). An ideal I of R is called S-multiplication if I is an S-multiplication R-module. A commutative ring R is called an S-multiplication ring if each ideal of R is S-multiplication. We characterize some special rings such as multiplication rings, almost multiplication rings, arithmetical ring, and S-P IR. Moreover, we generalize some properties of multiplication rings to S-multiplication rings and we study the transfer of this notion to various context of commutative ring extensions such as trivial ring extensions and amalgamated algebras along an ideal.

• Kyungpook Mathematical Journal
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• v.12 no.1
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• pp.9-12
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• 1972

• Journal of Korean Society of Forest Science
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• v.88 no.4
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• pp.454-461
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• 1999

The dynamics of root system in the fairy rings of Tricholoma matsutake was investigated in four zones divided into 'zone of decayed mycorrhizae', 'zone of mycorrhizae for fruiting', 'zone of physiologically active mycorrhizae' and 'zone of roots free from mycorrhizal infection'. The roots of Pinus densiflora in fairy rings, which occupied 70% of upper crown, comprised about 60% and 87% of total roots and alive roots, respectively. The ratio of fine-roots of P. densiflora over total roots was relatively higher than other species since that of P. densiflora was about 45% while that of the other species was about 13% on research of fine-roots. Especially, the roots of pine comprised about 70% of total root in the zone of mycorrhizae for fruiting and the zone of physiologically active mycorrhizae, which indicated that the pine roots were closely related to the fairy rings of T. matsutake. The fine roots of P. densiflora in the zone of physiologically active mycorrhizae was about 60.7%(1,087mg/100g soil) which was about twice compared to that of other zones. It allowed us to suppose that the fine roots of P. densiflora can make active growth in the zone of physiologically active mycorrhizae, and the growth was promoted by the fairy ring formation of T. matsutake. In addition, we found 3~5 times higher amount of fine roots than that of medium roots of P. densiflora in this zone, which indicated that the fairy rings of T. matsutake locate in the region of active growth of P. densiflora' roots.

• Bulletin of the Korean Mathematical Society
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• v.50 no.5
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• pp.1513-1521
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• 2013

In this paper we will study cyclic codes over some special rings: $\mathbb{F}_q[u]/(u^i)$, $\mathbb{F}_q[u_1,{\ldots},u_i]/(u^2_1,u^2_2,{\ldots},u^2_i,u_1u_2-u_2u_1,{\ldots},u_ku_j-u_ju_k,{\ldots})$, and $\mathbb{F}_q[u,v]/(u^i,v^j,uv-vu)$, where $\mathbb{F}_q$ is a field with $q$ elements $q=p^r$ for some prime number $p$ and $r{\in}\mathbb{N}-\{0\}$.

• Bulletin of the Korean Mathematical Society
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• v.42 no.3
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• pp.527-534
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• 2005

We consider countable rings with ascending chain condition on right annihilators. We determine the structure of a countable right p-injective Baer ring, a countable semi prime quasi-Baer ring and a countable quasi-Baer biregular ring.