• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1105-1115
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• 2022

The main objective of this paper is to introduce the notion of AMR-algebra and its generalization, and to compare them with other algebras such as BCK, BCI, BCH, · · ·, etc. We show moreover that the K-part of AMR-algebra is an abelian group, and the weak AMR-algebra is also an abelian group and generalizes many known algebras like BCI, BCH, and G.

• Korean Journal of Mathematics
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• v.30 no.3
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• pp.555-560
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• 2022

Suppose L/K be a finite abelian extension of number fields of odd degree and suppose an abelian variety A defined over L is a K-variety. If the endomorphism algebra of A/L is a field F, the followings are equivalent : (1) The enodomorphiam algebra of the restriction of scalars from L to K is simple. (2) There is no proper subfield of L containing L^G_F on which A has a K-variety descent.

• Journal of applied mathematics & informatics
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• v.40 no.3_4
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• pp.795-805
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• 2022

The aim of author's in this paper is to study the Cayley graph in the realm of signed graph. Moreover, we have characterized generating sets and finite abelian groups that corresponds to balanced Cayley signed graphs. The notion of Cayley signed graph has been demonstrated with the ample number of examples.

• Journal of applied mathematics & informatics
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• v.42 no.3
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• pp.521-538
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• 2024

In this paper, using the notion of the imprecise set, the idea of an imprecise group is introduced including some examples. The two key rules of classical set theory are obeyed by this extended version of fuzzy sets, which the existing complement definition of a fuzzy set failed to do. With the support from general group theory, the paper also provides some fundamental properties of an imprecise group here. Additionally, it includes a few characteristics of imprecise subgroups, and abelian imprecise group.

• Bulletin of the Korean Mathematical Society
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• v.13 no.2
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• pp.85-92
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• 1976

• Kyungpook Mathematical Journal
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• v.18 no.1
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• pp.11-15
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• 1978

• KSII Transactions on Internet and Information Systems (TIIS)
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• v.12 no.2
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• pp.764-785
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• 2018

In this paper, we present a new public key encryption scheme with equality test (PKEwET). Compared to other PKEwET schemes, we find that its security can be improved since the proposed scheme is based on non-Abelian factorization problems. To our knowledge, it is the first scheme regarding equality test that can resist quantum algorithm attacks. We show that our scheme is one-way against chosen-ciphertext attacks in the case that the computational Diffie-Hellman problem is hard for a Type-I adversary. It is indistinguishable against chosen-ciphertext attacks in the case that the Decisional Diffie-Hellman problem is hard in the random oracle model for a Type-II adversary. To conclude the paper, we demonstrate that our scheme is more efficient.

• Journal of the Korean Mathematical Society
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• v.50 no.2
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• pp.307-330
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• 2013

If $m$ and $n$ are non-negative integers, then three new classes of abelian $p$-groups are defined and studied: the $m$, $n$-simply presented groups, the $m$, $n$-balanced projective groups and the $m$, $n$-totally projective groups. These notions combine and generalize both the theories of simply presented groups and $p^{w+n}$-projective groups. If $m$, $n=0$, these all agree with the class of totally projective groups, but when $m+n{\geq}1$, they also include the $p^{w+m+n}$-projective groups. These classes are related to the (strongly) n-simply presented and (strongly) $n$-balanced projective groups considered in [15] and the n-summable groups considered in [2]. The groups in these classes whose lengths are less than ${\omega}^2$ are characterized, and if in addition we have $n=0$, they are determined by isometries of their $p^m$-socles.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1181-1198
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• 2022

In this paper we are concerned with the number of fuzzy subgroups of a finite abelian p-group ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ of rank three with order p^m+n+ℓ. We obtain a recurrence relation for the number of fuzzy subgroups of a finite abelian p-group ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ. In order to show that using this recurrence relation, one can find explicit formulas for the number of fuzzy subgroups of ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ consecutively, we give explicit formulas for the number of fuzzy subgroups of ℤ_p^m × ℤ_pⁿ × ℤ_p^ℓ where (n, ℓ) = (1, 1), (2, 1), (3, 1), (4, 1), (5, 1), (2, 2), (3, 2), (4, 2), (5, 2).

• Journal of the Korean Mathematical Society
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• v.12 no.1
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• pp.13-27
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• 1975