• Communications of the Korean Mathematical Society
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• v.23 no.4
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• pp.461-468
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• 2008

We define an $\epsilon$-fuzzy congruence, which is a weakened fuzzy congruence, find the $\epsilon$-fuzzy congruence generated by the union of two $\epsilon$-fuzzy congruences on a semigroup, and characterize the $\epsilon$-fuzzy congruences generated by fuzzy relations on semigroups. We also show that the collection of all $\epsilon$-fuzzy congruences on a semigroup is a complete lattice and that the collection of $\epsilon$-fuzzy congruences under some conditions is a modular lattice.

• 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.

• Journal of the Korean Mathematical Society
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• v.59 no.5
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• pp.945-962
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• 2022

For a positive integer ℓ, $\bar{A}_{\ell}(n)$ denotes the number of over-partitions of n into parts not divisible by ℓ. In this article, we find certain Ramanujan-type congruences for $\bar{A}_{r{\ell}}(n)$, when r ∈ {8, 9} and we deduce infinite families of congruences for them. Furthermore, we also obtain Ramanujan-type congruences for $\bar{A}_{13}(n)$ by using an algorithm developed by Radu and Sellers [15].

• Honam Mathematical Journal
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• v.28 no.1
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• pp.1-22
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• 2006

First, we obtain some results of intuitionistic fuzzy congruences on a regular semigroups contained in ($XH,\;XH^c$). Secondly, we introduce the concept of intuitionistic fuzzy idempotent separating congruences on a semigroup and investigate some of it's properties.

• Communications of the Korean Mathematical Society
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• v.29 no.1
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• pp.1-8
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• 2014

In this paper, we give congruences on an abundant semigroup with a quasi-ideal S-adequate transversal $S^{\circ}$ by the congruence pair abstractly which consists of congruences on the structure component parts R and ${\Lambda}$. We prove that the set of all congruences on this kind of semigroups is a complete lattice.

• Journal of the Korean Institute of Intelligent Systems
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• v.16 no.3
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• pp.357-366
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• 2006

We introduce the notion of intuitionistic fuzzy (t, s)-congruences on a lattice and study some of its properties. Moreover, we obtain some properties of intuitionistic fuzzy congruences on the direct product of two lattices. Finally, we prove that the set of all intuitionistic fuzzy congruences on a lattice forms a distributive lattice.

• Korean Journal of Mathematics
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• v.22 no.4
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• pp.683-691
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• 2014

We redefine a fuzzy congruence, discuss some properties of the fuzzy congruences, find the fuzzy congruence generated by a fuzzy relation on a semigroup, and give some lattice theoretic properties of the fuzzy congruences on semigroups.

• Journal of applied mathematics & informatics
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• v.40 no.5_6
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• pp.1003-1019
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• 2022

In this paper, by using the multiple fermionic p-adic integrals, we obtain Kummer-type congruences for the higher order Euler numbers and polynomials.

• East Asian mathematical journal
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• v.21 no.2
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• pp.241-248
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• 2005

Properties of congruences on n-ary groups are investigated.

• Communications of the Korean Mathematical Society
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• v.27 no.3
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• pp.477-482
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• 2012

In this note, we investigate partition congruences for a certain type of partition function, which is named as the overcubic partition pairs in light of the literature. Let $\bar{cp}(n)$ be the number of overcubic partition pairs. Then we will prove the following congruences: $$\bar{cp}(8n+7){\equiv}0(mod\;64)\;and\;\bar{cp}(9m+3){\equiv}0(mod\;3)$$.