• Journal of the Korean Mathematical Society
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• v.52 no.1
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• pp.67-80
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• 2015

For a pomonoid S, let us denote Pos-S the category of S-posets and S-poset maps. In this paper, we consider the slice category Pos-S/B for an S-poset B, and study some categorical ingredients. We first show that there is no non-trivial injective object in Pos-S/B. Then we investigate injective objects with respect to the class of regular monomorphisms in this category and show that Pos-S/B has enough regular injective objects. We also prove that regular injective objects are retracts of exponentiable objects in this category. One of the main aims of the paper is to draw attention to characterizing injectivity in the category Pos-S/B under a particular case where B has trivial action. Among other things, we also prove that the necessary condition for a map (an object) here to be regular injective is being convex and present an example to show that the converse is not true, in general.

• Bulletin of the Korean Mathematical Society
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• v.46 no.6
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• pp.1041-1050
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• 2009

Let R be a ring and ${\alpha}$ a monomorphism of R. We study the skew Laurent polynomial rings R[x, x$^{-1}$; ${\alpha}$] over an ${\alpha}$-skew Armendariz ring R. We show that, if R is an ${\alpha}$-skew Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x$^{-1}$; ${\alpha}$] is a Baer (resp. p.p.-) ring. Consequently, if R is an Armendariz ring, then R is a Baer (resp. p.p.-)ring if and only if R[x, x$^{-1}$] is a Baer (resp. p.p.-)ring.

• Kyungpook Mathematical Journal
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• v.55 no.4
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• pp.817-826
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• 2015

Let R be a commutative ring with total quotient ring K. Each monomorphic R-module endomorphism of a cyclic R-module is an isomorphism if and only if R has Krull dimension 0. Each monomorphic R-module endomorphism of R is an isomorphism if and only if R = K. We say that R has property (${\star}$) if for each nonzero element $a{\in}R$, each monomorphic R-module endomorphism of R/Ra is an isomorphism. If R has property (${\star}$), then each nonzero principal prime ideal of R is a maximal ideal, but the converse is false, even for integral domains of Krull dimension 2. An integral domain R has property (${\star}$) if and only if R has no R-sequence of length 2; the "if" assertion fails in general for non-domain rings R. Each treed domain has property (${\star}$), but the converse is false.

• East Asian mathematical journal
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• v.14 no.2
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• pp.259-268
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• 1998

In this paper, for a commutative ring R with an identity, considering the endomorphism ring $End_R$(M) of left R-module $_RM$ which is (quasi-)injective or (quasi-)projective, some discriminations of prime endomorphism were found as follows: each epimorphism with the irreducible(or simple) kernel on a (quasi-)injective module and each monomorphism with maximal image on a (quasi-)projective module are prime. It was shown that for a field F, any given square matrix in $Mat_{n{\times}n}$(F) with maximal image and irreducible kernel is a prime matrix, furthermore, any given matrix in $Mat_{n{\times}n}$(F) for any field F can be factored into a product of prime matrices.

• Communications of the Korean Mathematical Society
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• v.15 no.3
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• pp.453-467
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• 2000

For any S-flat module RM(which will be called endoflat) with a commutaitve ring R with identity, where S is the endomorphism ring RM, the fact that every epimorphism is an automorphism has been proved and the Jacobson Radical Rad(S) of S is described as follow; Rad(S) = { f$\in$S｜Imf=Mf is small in M} = {f$\in$S｜Imf $\leq$Rad(M)}. Additionally for any quasi-injective endo-flat module RM, the fact that every monomorphism is an automorphism has been proved and the Jacobson Radical Rad(S) for any quasi-injective endo-flat module has been studied too. Also some equivalent conditions for the semi-primitivity of any faithful endo-flat module RM with the open Jacobson Radical Rad(M) and those for the semi-simplicity of any faithful endo-flat quasi-injective module RM with the closed Socle Soc(M) have been studied.

• Plant Resources
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• v.3 no.3
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• pp.211-218
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• 2000

Intraspecific genetic relationship of 19 variation types of the Yam (Dioscorea alata) classified by their external morphological characteristics such as leaf and tuber shape were assessed by DNA using random and specific primer. Twenty two out of 113 primers (100 random[10-mer] primers, two 15 mer [M13 core sequence, and (GGAT)$_4$ sequence]) had been used in PCR-amplification. Only 12 primers, however, were success in DNA amplification in all of the analyzed plants, resulting in 93 randomly and specifically amplified DNA fragments. The analyzed taxa showed very high polymorphisms(69 bands, 71.0 %), allowing individual taxon to be identified based on DNA fingerprinting. Monomorphic bands among total amplified DNA bands of each primer was low under the 50%. Similarity indices between accessions were computed from PCR(polymerase chain reaction) data, and genetic relationships among intraspecific variations were closely related at the levels ranging from 0.66 to 0.90. These DNA data were not matched well with those of morphological characters since they were divided into two major groups at the similarity coefficient value of 0.70. Therefore, Grouping of species into variation types by mainly morphological charactistics was suggested unreasonable.

• Journal of Plant Biotechnology
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• v.31 no.1
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• pp.19-23
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• 2004

This study was conducted to observe the morphological characteristics and to analyse genetic relationship using RAPD markers in 9 species of Iris. The period of flowering was shown very broad among 9 species of Iris, from April 22 to June 9. The flower stalk was fluctuated from 9.0cm (I. rossii) to 104.0cm (I. ensata). I. ensata has the largest flower size and followed by I. laevigata, I. tectorum, I. sanguinea, I. pseudacorus, I. lactea, I. rossii, I. minutoaurea, I. odaesanensis. Among the 108 amplified bands by PCR with 8 random primers, 107 showed polymorphism and only one showed monomorphism among 9 species of Iris. The average dissimilarity coefficient among 9 species of Iris was 0.252. The range of dissimilarity coefficient was shown as from 0.095 to 0.609. Nine species were divided into three groups. The first group was I. tectorum, and the second group was I. lactea, I. laevigata, I. pseudacorus, I. odaesanensis. I. minutoaurea, I. rossii, I. sanguinea, I. ensata were belong to group three.

• Bulletin of the Korean Mathematical Society
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• v.56 no.2
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• pp.439-450
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• 2019

Let R be a ring with unity. Given modules $M_R$ and $_RN$, $M_R$ is said to be absolutely $_RN$-pure if $M{\otimes}N{\rightarrow}L{\otimes}N$ is a monomorphism for every extension $L_R$ of $M_R$. For a module $M_R$, the subpurity domain of $M_R$ is defined to be the collection of all modules $_RN$ such that $M_R$ is absolutely $_RN$-pure. Clearly $M_R$ is absolutely $_RF$-pure for every flat module $_RF$, and that $M_R$ is FP-injective if the subpurity domain of M is the entire class of left modules. As an opposite of FP-injective modules, $M_R$ is said to be a test for flatness by subpurity (or t.f.b.s. for short) if its subpurity domain is as small as possible, namely, consisting of exactly the flat left modules. Every ring has a right t.f.b.s. module. $R_R$ is t.f.b.s. and every finitely generated right ideal is finitely presented if and only if R is right semihereditary. A domain R is $Pr{\ddot{u}}fer$ if and only if R is t.f.b.s. The rings whose simple right modules are t.f.b.s. or injective are completely characterized. Some necessary conditions for the rings whose right modules are t.f.b.s. or injective are obtained.

• Journal of Korean Society of Forest Science
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• v.104 no.2
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• pp.187-192
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• 2015

Individuals in the population under a particular environmental condition influencing recurrently for a long time could locally adapted and local adaptation is of a fundamental importance in a breeding program, conservation activities of genetic resources or evolutionary biology. Plants at northern range limits have higher probability of expressing an adaptative genetic trait. The natural community at the northern range limit of Ilex cornuta (Chinese holly) in Buan, Jeollanam-do in Korea was composed of adults of 744 and seedlings of 211 (hereafter Community) and is designated as the Korean Natural Monument (No. 122) by the law. At two adjacent areas to Community, 85 (hereafter Plantation I) and 27 hollies (hereafter Plantation II) were planted respectively for preparations of the next generation. Eighty-five trees were sampled for genetic analysis in the three groups. Fifty-two (36%) of the total 143 amplicons were polymorphic from four AFLP primer combinations. A total of thirteen genotypes was identified and just one genotype was for 52 trees of Community. Seven and five genotypes were shown for Plantation I and II, respectively. There was no identical genotype between Community and Plantation (I or II) or between two plantation groups. Number of private loci was 2 for Community, 6 for Plantation I and 4 for Plantation II. We presumed their genetic backgrounds were quite different with one another and the plantation groups were made independently because they were different not only the genetic compositions but also their ages. Considering the genetic monomorphism by AFLP markers, observations of only male trees and asexual propagation as layerage or cuttage, the hollies in Community might be a genet by root suckering from a single male tree, not the results of selective removal of female trees for ornamental use in the past.

• Korean Journal of Plant Taxonomy
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• v.47 no.4
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• pp.297-303
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• 2017

In central and southern Korea, the two small insectivorous, terrestrial herbs, Utricularia bifida and U. caerulea, often co-occur at wet locations (or in wetlands). The Korean Peninsula (with central China and northern Japan) constitutes the northern edge of their distribution, as their main range is subtropical and tropical Asia. The Korean populations of both species are very likely of post-glacial origin, given that warm-temperate vegetation was absent from the Korean Peninsula during the Last Glacial Maximum. Two hypotheses of the post-glacial colonization of the peninsula can be formulated; first, if current populations were founded by propagules coming from a single ancestral population (i.e., a single refugium), we would expect low levels of genetic diversity. Alternatively, if contemporary Korean populations originated from multiple sources (multiple refugia), we would expect high levels of genetic variation. To test which is more likely, we surveyed the degree of allozyme variation at 20 loci in ten populations for each of the two species from southern Korea. We found no allozyme variation within each species. However, their aquatic congener U. australis exhibited allozyme polymorphism across Japan (four polymorphic loci at three enzyme systems). We suggest that southern Korean populations of Utricularia bifida and U. caerulea were established by a single introduction event from a genetically depauperate ancestral population.