• The Pure and Applied Mathematics
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• v.30 no.4
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• pp.397-406
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• 2023

Let R be a commutative ring with identity, X be an indeterminate over R, and R[X] be the polynomial ring over R. In this paper, we study when R[X] is a radically principal ideal ring. We also study the t-operation analog of a radically principal ideal domain, which is said to be t-compactly packed. Among them, we show that if R is an integrally closed domain, then R[X] is t-compactly packed if and only if R is t-compactly packed and every prime ideal Q of R[X] with Q ∩ R = (0) is radically principal.

• Journal of the Korean Mathematical Society
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• v.48 no.1
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• pp.191-205
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• 2011

It is well known that for a Krull domain R, the divisor class group of R is a torsion group if and only if every subintersection of R is a ring of quotients. Thus a natural question is that under what conditions, for a non-Krull domain R, every (t-)subintersection (resp., t-linked overring) of R is a ring of quotients or every (t-)subintersection (resp., t-linked overring) of R is at. To address this question, we introduce the notions of *-compact packedness and *-coprime packedness of (an ideal of) an integral domain R for a star operation * of finite character, mainly t or w. We also investigate the t-theoretic analogues of related results in the literature.

• Journal of the Korean earth science society
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• v.27 no.5
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• pp.548-556
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• 2006

The purpose of this study is to clarify the relict landform development of fluvial terrace and the soil characteristics occurring on the fluvial deposits. The physico-chemical properties of soil that are developed on terrace deposits and X-ray diffraction analysis of clay were investigated specifically. The horizon of $A_1$ consists of silt loam with reddish-brown color (5YR4/3). Its soil structures is a weak, fine, subangular, and blocky, breaking to granular. The horizon of $B_{1t}\;and\;B_{2t}$ are silt clay with either a yellowish red (5YR5/6), bright red (2.5YR4/6) color. This soil structure is weak, subangular, and blocky, with thin discontinuous bright red (2.5YR4/6) clay cutans and soft manganese concretions. This red soil structure is made on heavy-textures. It is packed compactly with parent materials of high fluvial surface sediments, and usually has a $A_1-B_{1t}-B_{2t}-C$ profile, from top to bottom. In most cases, clay accumulation in the B-horizon and clay cutans on ped surfaces are observed, which means the argillic horizon has formed. The soils derived from fluvial surface deposits are associated with soils. The soils on the high fluvial surface are considered to be a kind of paleo-red soil which were developed by strong desilicification and rubefaction, and strong leaching of bases under warmer bio-climatic condition during the old Pleistocene period. According to these morphological and anlaytical characteristics,geomorphological features and bio-climatic conditions under which the soil have developed on the high terrace sediment indicate that the soil should be classified as paleo-red soils.