• Kyungpook Mathematical Journal
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• v.11 no.1
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• pp.17-20
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• 1971

• 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.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.

• 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].