• Kyungpook Mathematical Journal
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• v.34 no.2
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• pp.223-225
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• 1994

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1689-1696
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• 2014

Recently, it was proved that every p-Schur ring over an abelian group of order $p^3$ is Schurian. In this paper, we prove that every commutative p-Schur ring over a non-abelian group of order $p^3$ is Schurian.

• Bulletin of the Korean Mathematical Society
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• v.52 no.3
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• pp.935-946
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• 2015

The purpose of this paper is to introduce a new class of rings that is closely related to the classes of pseudo valuation rings (PVRs) and pseudo-almost valuation domains (PAVDs). A commutative ring R is said to be ${\phi}$-ring if its nilradical Nil(R) is both prime and comparable with each principal ideal. The name is derived from the natural map ${\phi}$ from the total quotient ring T(R) to R localized at Nil(R). A prime ideal P of a ${\phi}$-ring R is said to be a ${\phi}$-pseudo-strongly prime ideal if, whenever $x,y{\in}R_{Nil(R)}$ and $(xy){\phi}(P){\subseteq}{\phi}(P)$, then there exists an integer $m{\geqslant}1$ such that either $x^m{\in}{\phi}(R)$ or $y^m{\phi}(P){\subseteq}{\phi}(P)$. If each prime ideal of R is a ${\phi}$-pseudo strongly prime ideal, then we say that R is a ${\phi}$-pseudo-almost valuation ring (${\phi}$-PAVR). Among the properties of ${\phi}$-PAVRs, we show that a quasilocal ${\phi}$-ring R with regular maximal ideal M is a ${\phi}$-PAVR if and only if V = (M : M) is a ${\phi}$-almost chained ring with maximal ideal $\sqrt{MV}$. We also investigate the overrings of a ${\phi}$-PAVR.

• Bulletin of the Korean Mathematical Society
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• v.50 no.1
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• pp.11-24
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• 2013

Let m and n be fixed positive integers and M a right R-module. Recall that M is said to be ($m$, $n$)-injective if $Ext^1$(P, M) = 0 for any ($m$, $n$)-presented right R-module P; M is said to be ($m$, $n$)-flat if $Tor_1$(N, P) = 0 for any ($m$, $n$)-presented left R-module P. In terms of some derived functors, relative injective or relative flat resolutions and dimensions are investigated. As applications, some new characterizations of von Neumann regular rings and p.p. rings are given.

• Bulletin of the Korean Mathematical Society
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• v.58 no.1
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• pp.195-204
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• 2021

Let R be a G-graded commutative ring with a nonzero unity and P be a proper graded ideal of R. Then P is said to be a graded uniformly pr-ideal of R if there exists n ∈ ℕ such that whenever a, b ∈ h(R) with ab ∈ P and Ann(a) = {0}, then bn ∈ P. The smallest such n is called the order of P and is denoted by ordR(P). In this article, we study the characterizations on this new class of graded ideals, and investigate the behaviour of graded uniformly pr-ideals in graded factor rings and in direct product of graded rings.

• Korean Journal of Mathematics
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• v.28 no.2
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• pp.241-255
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• 2020

Let 𝔽_q be the finite field with q = p^m elements. A complex valued Cohn function defined on 𝔽_q is introduced in [1]. In this paper we define generalized Cohn functions on Galois rings and investigate their properties.

• Journal of the Korean Mathematical Society
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• v.44 no.6
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• pp.1267-1279
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• 2007

For a ring endomorphism ${\alpha}$ and an ${\alpha}-derivation\;{\delta}$ of a ring R, we study relation between the set of annihilators in R and the set of annihilators in nearring $R[x;{\alpha},{\delta}]\;and\;R_0[[x;{\alpha}]]$. Also we extend results of Armendariz on the Baer and p.p. conditions in a polynomial ring to certain analogous annihilator conditions in a nearring of skew polynomials. These results are somewhat surprising since, in contrast to the skew polynomial ring and skew power series case, the nearring of skew polynomials and skew power series have substitution for its "multiplication" operation.

• Korean Journal of Mathematics
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• v.23 no.1
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• pp.163-169
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• 2015

We give idempotent generators for quadratic residue codes over p-adic integers and over the rings $\mathbb{Z}_{p^e}$.

• Kyungpook Mathematical Journal
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• v.46 no.4
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• pp.603-613
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• 2006

Near-rings considered are right near-rings and R is a near-ring. $J_0^r(R)$, the right Jacobson radical of R of type-0, was introduced and studied by the present authors. In this paper $J_1^r(R)$ and $J_2^r(R)$, the right Jacobson radicals of R of type-1 and type-2 are introduced. It is proved that both $J_1^r$ and $J_2^r$ are radicals for near-rings and $J_0^r(R){\subseteq}J_1^r(R){\subseteq}J_2^r(R)$. Unlike the left Jacobson radical classes, the right Jacobson radical class of type-2 contains $M_0(G)$ for many of the finite groups G. Depending on the structure of G, $M_0(G)$ belongs to different right Jacobson radical classes of near-rings. Also unlike left Jacobson-type radicals, the constant part of R is contained in every right 1-modular (2-modular) right ideal of R. For any family of near-rings $R_i$, $i{\in}I$, $J_{\nu}^r({\oplus}_{i{\in}I}R_i)={\oplus}_{i{\in}I}J_{\nu}^r(R_i)$, ${\nu}{\in}\{1,2\}$. Moreover, under certain conditions, for an invariant subnear-ring S of a d.g. near-ring R it is shown that $J_2^r(S)=S{\cap}J_2^r(R)$.

• Korean Journal of Environmental Agriculture
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• v.30 no.3
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• pp.229-233
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• 2011

BACKGROUND: Soil acidification, which is known to be one of the reasons of forest decline, is associated with decreases in exchangeable Ca and increases in Al concentration, leading to low Ca/Al ratio in soil solution. As tree rings are datable archives of environmental changes, Ca/Al ratios of annual growth ring may show decreasing pattern in accordance with the progress of soil acidification. This study was conducted to investigate Ca/Al pattern of Pinus densiflora tree ring in an attempt to test its usefulness as an indicator of historical soil acidification. METHODS AND RESULTS: Three P. densiflora tree disks were collected from P. densiflora forests in Jeonnam province, and soil samples (0-10, 10-20, and 20-30 cm in depth) were also collected from the tree locations. Soils were analyzed for pH and exchangeable Ca and Al concentrations, and Ca/Al was calculated. Annual growth rings formed between 1969 and 2007 were separated and analyzed for Ca/Al. Soil Ca/Al was positively (P<0.01) correlated with soil pH, suggesting that soil acidification decreased Ca while increasing Al availability, lowering Ca/Al in soil solution. The Ca/Al of tree rings also showed a decreasing pattern from 18.2 to 5.5 during the period, and this seemed to reflect historical acidification of the soils. CONCLUSION(s): The relationship between soil pH and Ca/Al and the decreasing pattern of Ca/Al of tree ring suggest that Ca/Al of tree ring needs to be considered as a proxy of the progress of soil acidification in P. densiflora forest in southern Korea.