• Bulletin of the Korean Mathematical Society
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• v.45 no.4
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• pp.757-762
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• 2008

In this paper, we generalize a few results of [7, 10] for lower radical classes of rings, by using the limit ordinal construction for lower radical classes of hemirings.

• Kyungpook Mathematical Journal
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• v.19 no.2
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• pp.205-211
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• 1979

In this paper we continue the study of formation radical (F-radical) classes initiated in [3]. Hereditary and stronger properties of F-radical classes are discussed by giving construction for lower hereditary, lower stronger and lower strongly hereditary F-radical classes containing a given class M. It is shown that the Baer F-radical B is the lower strongly hereditary F-radical class containing the class of all nilpotent ideals and it is the upper radical class with $\{(I,\;N){\mid}N{\in}C,\;N\;is\;prime\}{\subset}SB$ where SB denotes the semisimple F-radical class of B and C is an arbitrary but fixed class of homomorphically closed near-rings. The existence of a largest F-radical class contained in a given class is examined using the concept of complementary F-radical introduced by Scott [5].

• Kyungpook Mathematical Journal
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• v.43 no.4
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• pp.495-497
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• 2003

Let ${\wp}_1$, ${\wp}_2$ be the radical classes of rings. Y. Lee and R. E. Propes have defined their sum by ${\wp}_1+{\wp}_2=\{R{\in}{\omega}:{\wp}_1(R)+{\wp}_2(R)=R\}$. They have shown that ${\wp}_1+{\wp}_2$ is not a radical class in general. In this paper, a few results of Lee and Propes are generalized and also new conditions are investigated under which this sum becomes a radical class.

• Genomics & Informatics
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• v.8 no.4
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• pp.170-176
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• 2010

The Ribonucleotide reductases (RNR) are essential enzymes that catalyze the conversion of nucleotides to deoxynucleotides in DNA replication and repair in all living organisms. The RNRs operate by a free radical mechanism but differ in the composition of subunit, cofactor required and regulation by allostery. Based on these differences the RNRs are classified into three classesclass I, class II and class III which depend on oxygen, adenosylcobalamin and S-adenosylmethionine with an iron sulfur cluster respectively for radical generation. In this article thirty seven sequences belonging to each of the three classes of RNR were analyzed by using various tools of bioinformatics. Phylogenetic analysis, dot-plot comparisons and motif analysis was done to identify a number of differences in the three classes of RNRs. In this research article, we have attempted to decipher evolutionary relationship between the three classes of RNR by using bioinformatics approach.

• Kyungpook Mathematical Journal
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• v.48 no.4
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• pp.545-551
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• 2008

Necessary and sufficient conditions for a radical class of rings to satisfy the polynomial equation $\rho$(R[x]) = ($\rho$(R))[x] have been investigated. The interrelationsh of polynomial equation, Amitsur property and polynomial extensibility is given. It has been shown that complete analogy of R.E. Propes result for radicals of matrix rings is not possible for polynomial rings.

• Communications of the Korean Mathematical Society
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• v.38 no.4
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• pp.1191-1213
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• 2023

In this paper, we introduce and study two new classes of lightlike submersions, called radical transversal and transversal lightlike submersions between an indefinite Sasakian manifold and a lightlike manifold. We give examples and investigate the geometry of distributions involved in the definitions of these lightlike submersions. We also study radical transversal and transversal lightlike submersions from an indefinite Sasakian manifold onto a lightlike manifold with totally contact umbilical fibers.

• Kyungpook Mathematical Journal
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• v.13 no.1
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• pp.81-86
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• 1973

• Kyungpook Mathematical Journal
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• v.16 no.1
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• pp.49-52
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• 1976

• Kyungpook Mathematical Journal
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• v.19 no.1
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• pp.3-7
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• 1979

• 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 $J_2^r(S)=S{\cap}J_2^r(R)$.