• Korean Journal of Mathematics
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• v.11 no.2
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• pp.147-153
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• 2003

We investigate some properties on right(resp. left) duo $po$-semigroups.

• Journal for History of Mathematics
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• v.20 no.2
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• pp.109-126
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• 2007

This paper is to study theorems related with congruence of triangles in Lobachevskii's and Hadamard's geometry textbooks, and to compare their proof methods. We find out that Lobachevskii's geometry textbook contains 5 theorems of triangles' congruence, but doesn't explain congruence of right triangles. In Hadamard's geometry textbook description system of the theorems of triangles' congruence is similar with our mathematics textbook. Hadamard's geometry textbook treat 3 theorems of triangles' congruence, and 2 theorems of right triangles' congruence. But in Hadamard's geometry textbook all theorems are proved.

• Korean Journal of Mathematics
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• v.14 no.2
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• pp.241-248
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• 2006

We define a G-fuzzy congruence, which is a generalized fuzzy congruence, and characterize the G-fuzzy congruence generated by a left and right compatible fuzzy relation on a semigroup.

• Bulletin of the Korean Mathematical Society
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• v.36 no.1
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• pp.139-146
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• 1999

It is known that a right nilpotent congruence $\beta$ on a finite algebra A is also left nilpotent [3]. The question on whether the left nilpotency class of $\beta$ in less than or equal to the right nilpotency class of $\beta$is still open. In this paper we find an upper limit for the left nilpotency class of $\beta$. In addition, under the assumption that 1 $\in$ typ{A}, we show that $(\beta]^k=[\beta)^k$ for all k$\geq$1. Thus the left and right nilpotency classes of $\beta$ are the same in this case.

• Journal of the Chungcheong Mathematical Society
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• v.24 no.3
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• pp.449-456
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• 2011

In this paper, we considered the congruence relation, isomorphism and obtained some properties of HS-algebras.

• The Pure and Applied Mathematics
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• v.4 no.2
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• pp.131-135
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• 1997

We give the relation between the semilattice congruence N and the set of prime ideals of the ordered $\Gamma$-semigroup M.

• Communications of the Korean Mathematical Society
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• v.19 no.1
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• pp.1-10
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• 2004

We here consider necessary and sufficient conditions for a completely right injective semigroup S whose lattice Ｌ(S) of right congruences on S is semiatomic. These are preceded by a number of results on the characterization of a semigroup S in which every automaton over S is injective(called a completely right injective semigroup).

• The Mathematical Education
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• v.46 no.3
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• pp.273-292
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• 2007

The purpose of this study was to find out how second, fourth and sixth graders understood the main contents related to spatial sense in the Seventh National Mathematics Curriculum. For this purpose, this study examined students' understanding of the main contents of congruence transformation (slide, flip, turn), mirror symmetry, cubes, congruence and symmetry. An investigation was conducted and the subjects included 483 students. The main results are as follows. First, with regards to congruence transformation, whereas students had high percentages of correct answers on questions concerning slide, they had lower percentages on questions concerning turn. Percentages of correct answers on flip questions had significant differences among the three grades. In addition, most students experienced difficulties in describing the changes of shapes. Second, students understood the fact that the right and the left of an image in a mirror are exchanged, but they had poor overall understanding of mirror symmetry. The more complicated the cubes, the lower percentages of correct answers. Third, students had a good understanding of congruences, but they had difficulties in finding out congruent figures. Lastly, they had a poor understanding of symmetry and, in particular, didn't distinguish a symmetric figure of a line from a symmetric figure of a point.

• Journal of applied mathematics & informatics
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• v.9 no.1
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• pp.449-458
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• 2002

We shall give a gereralization for a new right congruence induced by right congruences on S and right ideals of S and discuss the radicals associated with automata. Also we shall discuss the relationship between the collection of all right ideals in S and the collection of all right congruences on S.

• Journal of the Korean Institute of Intelligent Systems
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• v.17 no.1
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• pp.100-111
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• 2007

We introduce the concept of intuitionistic fuzzy G-equivalence relations (congruence), and we obtain some results. Furthermore, we prove that $IFC_G(K)$ is isomorphic to $IFN^*(K)$ for any group K. Also, we prove that($IFC_{G,({\lambda},{\mu})}/{\sim},\;*$) and ($IFNG_{({\lambda},{\mu})}(K),\;{\circ}$) are isomorphic.