• Bulletin of the Korean Mathematical Society
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• v.46 no.3
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• pp.591-598
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• 2009

This paper studies the relations between ideals, filters, regular congruences and normal congruences in inclines. It is shown that for any incline, there are a one-to-one correspondence between all ideals and all regular congruences and a one-to-one correspondence between all filters and all normal congruences.

• Bulletin of the Korean Mathematical Society
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• v.46 no.5
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• pp.873-884
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• 2009

We characterize QB-ideals of exchange rings by means of quasi-invertible elements and annihilators. Further, we prove that every $2\times2$ matrix over such ideals of a regular ring admits a diagonal reduction by quasi-inverse matrices. Prime exchange QB-rings are studied as well.

• Honam Mathematical Journal
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• v.35 no.2
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• pp.201-210
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• 2013

In this paper, we introduced the notion of multiplier of a BCC-algebra, and gave some properties of BCC-algebras. Also, we characterized kernels and normal ideals of multipliers on BCC-algebras.

• Kyungpook Mathematical Journal
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• v.45 no.2
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• pp.199-209
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• 2005

An ideal space is ${\cal{I}}-resolvable$ if it has two disjoint ${\cal{I}}-dense$ subsets. We answer the question: If X is ${\cal{I}}-resolvable$, then is X (${\cal{I}}\;{\cup}\;{\cal{N}$)-resolvable?, posed by Dontchev, Ganster and Rose. We give three generalizations of the well known Banach Category Theorem and deduce the Banach category Theorem as a corollary. Characterizations of completely codense ideals and ${\cal{I}-locally$ closed sets are given and their properties are discussed.