• Communications of the Korean Mathematical Society
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• v.10 no.4
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• pp.783-787
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• 1995

In this paper we characterize cancellation ideals in terms of multiplication ideals. Especially, we find a condition for an ideal generated by three elements to be a cancellation ideal.

• Bulletin of the Korean Mathematical Society
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• v.44 no.1
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• pp.151-156
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• 2007

A connection between weak ${\pi}-regularity$ and the condition every prime ideal is maximal will be investigated. We prove that a certain 2-primal ring R is weakly ${\pi}-regular$ if and only if every prime ideal is maximal. This result extends several known results nontrivially. Moreover a characterization of minimal prime ideals is also considered.

• Journal of applied mathematics & informatics
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• v.26 no.5_6
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• pp.1049-1056
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• 2008

Intuitionistic Fuzzifications of strong hyper K-ideals and hyper K-subalgebras in hyper K-algebras are discussed, and related properties are investigated. Relations between intuitionistic fuzzy hyper K-subalgebras, intuitionistic fuzzy weak hyper K-ideals and intuitionistic fuzzy strong hyper K-ideals are provided.

• Journal of applied mathematics & informatics
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• v.5 no.1
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• pp.269-275
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• 1998

We find the Hibert functions of basic configurations in $P^n$. In particular we obtain the minimal generators of the ideal of a weak-k-configuration in $P^n$.

• East Asian mathematical journal
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• v.23 no.2
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• pp.247-255
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• 2007

Basic properties of branches of weak BCC-algebras and ideals of BCC-algebras containing only atoms are described.

• Communications of the Korean Mathematical Society
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• v.23 no.3
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• pp.325-331
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• 2008

In this paper we introduce the notion of weakly prime left ideals in near-subtraction semigroups. Equivalent conditions for a left ideal to be weakly prime are obtained. We have also shown that if (M, L) is a weak $m^*$-system and if P is a left ideal which is maximal with respect to containing L and not meeting M, then P is weakly prime.

• Kyungpook Mathematical Journal
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• v.62 no.1
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• pp.29-41
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• 2022

We study the concept of a quasi-ideal and a generalized bi-ideal of an n-ary semigroup; give a construction of the quasi-ideal of an n-ary semigroup generated by its nonempty subset; and introduce the notions of regularities, namely, a left regularity and a left weakly regularity. Moreover, the notions of a right regularity, a right weak regularity and a complete regularity are given. Finally, characterizations of these regularities are presented.

• Bulletin of the Korean Mathematical Society
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• v.28 no.2
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• pp.175-180
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• 1991

In [3], [4] and [5], Hochster and Huneke introduced the notions of the tight closure of an ideal and of the weak F-regularity of a ring. This notion enabled us to give new proofs of many results in commutative algebra. A regular ring is known to be F-regular, and a Gorenstein local ring is proved to be F-regular provided that one ideal generated by a system of parameters (briefly s.o.p.) is tightly closed. In fact, a Gorenstein local ring is weakly F-regular if and only if there exists a system of parameters ideal which is tightly closed [3]. But we do not know whether this fact is true or not if a ring is not Gorenstein, in particular, a ring is a Cohen Macaulay (briefly C-M) local ring. In this paper, we will prove this in the case of an 1-dimensional C-M local ring. For this, we study the F-rationality and the normality of the ring. And we will also prove that a C-M local ring is to be Gorenstein under some additional condition about the tight closure.

• Journal of applied mathematics & informatics
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• v.6 no.1
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• pp.247-252
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• 1999

The purposed of this paper is to introduced some basic concepts of Galois connection between fuzzy ordered sets. And discuss its relations with the property of fuzzy ordered set.

• Journal of the Korea Institute of Information Security & Cryptology
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• v.12 no.1
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• pp.33-42
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• 2002

We present a systematic way to armor a zero-knowledge interactive proof based identification scheme that has badly chosen keys. Keys are sometimes mistakenly chosen to be weak(neither random nor long), and a weak key is often preferred to a strong key so that it might be easy for human to remember. Weak keys severely degrade the security of ZKIP based identification schemes. We show using off-line guessing attack how the weak key threats the security of ZlKIP based identification schemes. For the proper usage of ZKIP, we introduce a specialized form of ZKIP, which has a secret coin-tossing stage. Using the secret coin tossing, a secure framework is proposed for ZKIP based identification schemes with weak key in the ideal cipher model. The framework is very useful in password based authentication and key exchange protocol