• Korean Journal of Mathematics
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• v.17 no.3
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• pp.233-236
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• 2009

We investigate in this paper some equivalent conditions for right principally quasi-Baer rings to be reflexive. Using these results we are able to prove that if R is a reflexive right principally quasi-Baer ring then R is a left principally quasi-Baer ring. In addition, for an idempotent reflexive principally quasi-Baer ring R we show that R is prime if and only if R is torsion free.

• Communications of the Korean Mathematical Society
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• v.21 no.1
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• pp.1-9
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• 2006

A ring R is called (left principally) quasi-Baer if the left annihilator of every (principal) left ideal of R is generated by an idempotent. Let R be a ring, G be an ordered monoid acting on R by $\beta$ and R be G-compatible. It is shown that R is (left principally) quasi-Baer if and only if skew monoid ring $R_{\beta}[G]$ is (left principally) quasi-Baer. If G is an abelian monoid, then R is (left principally) quasi-Baer if and only if the Cohn-Jordan extension $A(R,\;\beta)$ is (left principally) quasi-Baer if and only if left Ore quotient ring $G^{-1}R_{\beta}[G]$ is (left principally) quasi-Baer.

• Bulletin of the Korean Mathematical Society
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• v.61 no.2
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• pp.301-315
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• 2024

Some results are generalized from principally injective rings to principally injective modules. Moreover, it is proved that the results are valid to some other extended injectivity conditions which may be defined over modules. The influence of such injectivity conditions are studied for both the trace and the reject submodules of some modules over commutative rings. Finally, a correction is given to a paper related to the subject.

• Journal of the Korean Mathematical Society
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• v.52 no.2
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• pp.269-331
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• 2015

For a fixed positive integer g, we let $\mathcal{P}_g=\{Y{\in}\mathbb{R}^{(g,g)}{\mid}Y=^tY>0\}$ be the open convex cone in the Euclidean space $\mathbb{R}^{g(g+1)/2}$. Then the general linear group GL(g, $\mathbb{R}$) acts naturally on $\mathcal{P}_g$ by $A{\star}Y=AY^tA(A{\in}GL(g,\mathbb{R}),\;Y{\in}\mathcal{P}_g)$. We introduce a notion of polarized real tori. We show that the open cone $\mathcal{P}_g$ parametrizes principally polarized real tori of dimension g and that the Minkowski modular space 𝔗g = $GL(g,\mathbb{Z}){\backslash}\mathcal{P}_g$ may be regarded as a moduli space of principally polarized real tori of dimension g. We also study smooth line bundles on a polarized real torus by relating them to holomorphic line bundles on its associated polarized real abelian variety.

• Journal of the Korean Mathematical Society
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• v.48 no.6
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• pp.1189-1201
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• 2011

Let R be a ring and M a right R-module, S = $End_R$(M). The module M is called almost principally small injective (or APS-injective for short) if, for any a ${\in}$ J(R), there exists an S-submodule $X_a$ of M such that $l_Mr_R$(a) = Ma $Ma{\bigoplus}X_a$ as left S-modules. If $R_R$ is a APS-injective module, then we call R a right APS-injective ring. We develop, in this paper, APS-injective rings as a generalization of PS-injective rings and AP-injective rings. Many examples of APS-injective rings are listed. We also extend some results on PS-injective rings and AP-injective rings to APS-injective rings.

• Journal of Korean Society of Rural Planning
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• v.3 no.1
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• pp.33-40
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• 1997

This paper reviews the differences between the selected village groves and the selected roadside groves. In Chonbuk province, the village groves were principally found in the east mountainous region and roadside groves were principally found in the west low-sloped region. They were located in the place of good accessibility and good view. The differrence between the village groves and roadside groves was considerately large in the aspect of physical, socio-behavioral condition and vegetation structure. Both were contrasted in many points. The results resolve itself into Table 2, 4, 6. This research is useful in finding the characters of the both groves and in preparing the conservation and management plan of the groves through comparative review.

• Kyungpook Mathematical Journal
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• v.51 no.2
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• pp.177-185
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• 2011

A right ideal I of a ring R is small in case for every proper right ideal K of R, K + I ${\neq}$ = R. A right R-module M is called PS-injective if every R-homomorphism f : aR ${\rightarrow}$ M for every principally small right ideal aR can be extended to R ${\rightarrow}$ M. A ring R is called right PS-injective if R is PS-injective as a right R-module. We develop, in this article, PS-injectivity as a generalization of P-injectivity and small injectivity. Many characterizations of right PS-injective rings are studied. In light of these facts, we get several new properties of a right GPF ring and a semiprimitive ring in terms of right PS-injectivity. Related examples are given as well.

• Kyungpook Mathematical Journal
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• v.57 no.3
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• pp.401-417
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• 2017

Ever since their introduction, skew PBW ($Poincar{\acute{e}}$-Birkhoff-Witt) extensions of rings have kept growing in importance, as researchers characterized their properties (such as primeness, Krull and Goldie dimension, homological properties, etc.) in terms of intrinsic properties of the base ring, and studied their relations with other fields of mathematics, as for example quantum mechanics theory. Many rings and algebras arising in quantum mechanics can be interpreted as skew PBW extensions. Our aim in this paper is to study skew PBW extensions of Baer, quasi-Baer, principally projective and principally quasi-Baer rings, in the case when the base ring R is not assumed to be reduced. We just impose some mild compatibleness over the base ring R, and prove that these properties are stable over this kind of extensions.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 1997.11a
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• pp.233-236
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• 1997

An investigation has been made of the various plasma chemistry reactions that occur in the corona discharge of an electrostatic precipitator operating in a typical flue gas. As the results of investigation, sulphur dioxide is removed principally by reactions with OH radicals to produce sulphuric acid, while nitrogen oxides are removed principally by reduction via the N radical to molecular nitrogen. If electrostatic precipitator\ulcorner used for flue gases are operated with positive voltages instead of negative dc voltages, there are significant reductions in the emission of the undesirable gases SO$_2$, NO, and NO$_2$. Thus, in this paper we design the bidirectional pulse generator for removal of flue gas, where the pulse width is more than 50[nsec] and the maximum output voltage is more than 100[kVl.

• Communications of the Korean Mathematical Society
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• v.23 no.1
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• pp.29-40
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• 2008

Here, some classes of regular order semigroups are discussed. We shall consider that the problems of the existences of (multiplicative) inverse $^{\delta}po$-transversals for such classes of po-semigroups and obtain the following main results: (1) Giving the equivalent conditions of the existence of inverse $^{\delta}po$-transversals for regular order semigroups (2) showing the order orthodox semigroups with biggest inverses have necessarily a weakly multiplicative inverse $^{\delta}po$-transversal. (3) If the Green's relation $\cal{R}$ and $\cal{L}$ are strongly regular (see. sec.1), then any principally ordered regular semigroup (resp. ordered regular semigroup with biggest inverses) has necessarily a multiplicative inverse $^{\delta}po$-transversal. (4) Giving the structure theorem of principally ordered semigroups (resp. ordered regular semigroups with biggest inverses) on which $\cal{R}$ and $\cal{L}$ are strongly regular.