• Communications of the Korean Mathematical Society
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• v.20 no.3
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• pp.457-466
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• 2005

We study in this note rings whose prime radicals are completely prime. We obtain equivalent conditions to the complete 2-primal-ness and observe properties of completely 2-primal rings, finding examples and counterexamples to the situations that occur naturally in the process.

• Journal of applied mathematics & informatics
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• v.33 no.5_6
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• pp.579-591
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• 2015

Properties of prime filters are studied in BE-algebras as well as in commutative BE-algebras. An equivalent condition is derived for a BE-algebra to become a totally ordered set. A condition L is introduced in a commutative BE-algebra in ordered to study some more properties of prime filters in commutative BE-algebras. A set of equivalent conditions is derived for a commutative BE-algebra to become a chain. Some topological properties of the space of all prime filters of BE-algebras are studied.

• Korean Journal of Mathematics
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• v.17 no.4
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• pp.495-505
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• 2009

By means of Green function and fixed point theorem related with cone theoretic method we show that there exist multiple nonnegative solutions of a Dirichlet problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\lambda}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x(0)=0=x(T)}$$, and a mixed problem $$\array{-[p(t)x^{\prime}(t)]^{\prime}={\mu}q(t)f(x(t)),\;t{\in}I=[0,\;T]\\x^{\prime}(0)=0=x(T)}$$, where ${\lambda}$ and ${\mu}$ are positive parameters.

• Journal of the Korean Mathematical Society
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• v.36 no.2
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• pp.369-380
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• 1999

As a continuation of the paper [3], in this paper we investigate the further properties on LI-ideals, and show that how to generate an LI-ideal by both and LI-ideal and an element. We define a prime LI-ideal, and give an equivalent condition for a proper LI-ideal to be prime. Using this result, we establish the extension property and prime LI-ideal theorem.

• Bulletin of the Korean Mathematical Society
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• v.39 no.3
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• pp.485-494
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• 2002

In this paper we will show that if there exist derivations D, G on a n!-torsion free semi-prime ring R such that the mapping $D^2+G$ is n-commuting on R, then D and G are both commuting on R. And we shall give the algebraic conditions on a ring that a Jordan derivation is zero.

• Communications of the Korean Mathematical Society
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• v.11 no.2
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• pp.315-321
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• 1996

Recently, N. Kehayopulu [4] introduced the concepts of weakly prime ideals of ordered semigroups. In this paper, we define the concepts of left(right) weakly prime and left(right) semiregular. Also we investigate the properties of them.

• Bulletin of the Korean Mathematical Society
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• v.51 no.6
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• pp.1805-1827
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• 2014

Let $\mathcal{K}^{\prime}_M$ be the generalized tempered distributions of $e^{M(t)}$-growth, where the function M(t) grows faster than any linear functions as ${\mid}t{\mid}{\rightarrow}{\infty}$, and let $K^{\prime}_M$ be the Fourier transform spaces of $\mathcal{K}^{\prime}_M$. We obtain the relationship between certain classes of analytic functions in tubes, $\mathcal{K}^{\prime}_M$ and $K^{\prime}_M$.

• Bulletin of the Korean Mathematical Society
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• v.43 no.3
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• pp.559-573
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• 2006

In this Paper three different types of fuzzy Prime ideals are introduced. Condition is obtained for a fuzzy 2-prime ideal will have two elements in its range. It has been shown that A is fuzzy 2-prime ideal of the semiring R if and only if 1-A is a fuzzy $m_2-system$ in R.

• Kyungpook Mathematical Journal
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• v.50 no.1
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• pp.117-122
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• 2010

In this paper, we introduce the concepts of 1-prime ideals and 2-prime ideals in semirings. We have also introduced $m_1$-system and $m_2$-system in semiring. We have shown that if Q is an ideal in the semiring R and if M is an $m_2$-system of R such that $\overline{Q}{\bigcap}M={\emptyset}$ then there exists as 2-prime ideal P of R such that Q $\subseteq$ P with $P{\bigcap}M={\emptyset}$.

• Proceedings of the IEEK Conference
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• 2000.11b
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• pp.136-139
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• 2000

In this paper, we propose a prime code and a new cryptographic algorithm for encryption and decryption as its application. The characteristics of prime numbers with irregular distribution and uniqueness are used to generate the prime code. Based on the prime code, an encryption algorithm for secret key is presented. Since the algorithm requires simpler operations than existing encryption such as DES, the burden for hardware implementation of the encryption and decryption process is alleviated.