• Title/Summary/Keyword: mathematical structures

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Mathematical Structures and SuanXue QiMeng (수학적(數學的) 구조(構造)와 산학계몽(算學啓蒙))

  • Hong, Sung Sa;Hong, Young Hee;Lee, Seung On
    • Journal for History of Mathematics
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    • v.26 no.2_3
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    • pp.123-130
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    • 2013
  • It is well known that SuanXue QiMeng has given the greatest contribution to the development of Chosun mathematics and that the topics and their presentation including TianYuanShu in the book have been one of the most important backbones in the developement. The purpose of this paper is to reveal that Zhu ShiJie emphasized decidedly mathematical structures in his SuanXue QiMeng, which in turn had a great influence to Chosun mathematicians' structural approaches to mathematics. Investigating structural approaches in Chinese mathematics books before SuanXue QiMeng, we conclude that Zhu's attitude to mathematical structures is much more developed than his precedent ones and that his mathematical structures are very close to the present ones.

Mathematical Structures of Joseon mathematician Hong JeongHa (조선(朝鮮) 산학자(算學者) 홍정하(洪正夏)의 수학적(數學的) 구조(構造))

  • Hong, Sung Sa;Hong, Young Hee;Lee, Seung On
    • Journal for History of Mathematics
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    • v.27 no.1
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    • pp.1-12
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    • 2014
  • From the mid 17th century, Joseon mathematics had a new beginning and developed along two directions, namely the traditional mathematics and one influenced by western mathematics. A great Joseon mathematician if not the greatest, Hong JeongHa was able to complete the Song-Yuan mathematics in his book GuIlJib based on his studies of merely Suanxue Qimeng, YangHui Suanfa and Suanfa Tongzong. Although Hong JeongHa did not deal with the systems of equations of higher degrees and general systems of linear congruences, he had the more advanced theories of right triangles and equations together with the number theory. The purpose of this paper is to show that Hong was able to realize the completion through his perfect understanding of mathematical structures.

SOME COMMUTATIVE RINGS DEFINED BY MULTIPLICATION LIKE-CONDITIONS

  • Chhiti, Mohamed;Moindze, Soibri
    • Bulletin of the Korean Mathematical Society
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    • v.59 no.2
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    • pp.397-405
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    • 2022
  • In this article we investigate the transfer of multiplication-like properties to homomorphic images, direct products and amalgamated duplication of a ring along an ideal. Our aim is to provide examples of new classes of commutative rings satisfying the above-mentioned properties.

A Study on the Manifestation of Tacit Knowledge through Exemplification (예 구성 활동을 통한 암묵적 지식의 현시에 관한 연구)

  • Lee, Keun-Bum;Lee, Kyeong-Hwa
    • School Mathematics
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    • v.18 no.3
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    • pp.571-587
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    • 2016
  • Nam(2008a) suggested that the role of teacher for helping students to learn mathematical structures should be the manifestor of tacit knowledge. But there have been lack of researches on embodying the manifestation of tacit knowledge. This study embodies the manifestation of tacit knowledge by showing that exemplification is one way of manifestation of tacit knowledge in terms of goal, contents, and method. First, the goal of the manifestation of tacit knowledge through exemplification is helping students to learn mathematical structures. Second, the manifestation of tacit knowledge through exemplification intends to teach students mathematical structures in the tacit dimension by perceiving invariance in the midst of change. Third, the manifestation of tacit knowledge through exemplification intends to teach students mathematical structures in the tacit dimension by constructing explicit knowledge creatively, reflection on constructive activity and social interaction. In conclusion, exemplification could be seen one way of embodying the manifestation of tacit knowledge in terms of goal, contents, and method.

Mathematical Structures of Polynomials in Jeong Yag-yong's Gugo Wonlyu (정약용(丁若鏞)의 산서(算書) 구고원류(勾股源流)의 다항식(多項式)의 수학적(數學的) 구조(構造))

  • Hong, Sung Sa;Hong, Young Hee;Lee, Seung On
    • Journal for History of Mathematics
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    • v.29 no.5
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    • pp.257-266
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    • 2016
  • This paper is a sequel to our paper [3]. Although polynomials in the tianyuanshu induce perfectly the algebraic structure of polynomials, the tianyuan(天元) is always chosen by a specific unknown in a given problem, it can't carry out the role of the indeterminate in ordinary polynomials. Further, taking the indeterminate as a variable, one can study mathematical structures of polynomials via those of polynomial functions. Thus the theory of polynomials in East Asian mathematics could not be completely materialized. In the previous paper [3], we show that Jeong Yag-yong disclosed in his Gugo Wonlyu(勾股源流) the mathematical structures of Pythagorean polynomials, namely polynomials p(a, b, c) where a, b, c are the three sides gou(勾), gu(股), xian(弦) of a right triangle, respectively. In this paper, we show that Jeong obtained his results through his recognizing Pythagorean polynomials as polynomial functions of three variables a, b, c.

Division Algorithm in SuanXue QiMeng

  • Hong, Sung Sa;Hong, Young Hee;Lee, Seung On
    • Journal for History of Mathematics
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    • v.26 no.5_6
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    • pp.323-328
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    • 2013
  • The Division Algorithm is known to be the fundamental foundation for Number Theory and it leads to the Euclidean Algorithm and hence the whole theory of divisibility properties. In JiuZhang SuanShu(九章算術), greatest common divisiors are obtained by the exactly same method as the Euclidean Algorithm in Elements but the other theory on divisibility was not pursued any more in Chinese mathematics. Unlike the other authors of the traditional Chinese mathematics, Zhu ShiJie(朱世傑) noticed in his SuanXue QiMeng(算學啓蒙, 1299) that the Division Algorithm is a really important concept. In [4], we claimed that Zhu wrote the book with a far more deeper insight on mathematical structures. Investigating the Division Algorithm in SuanXue QiMeng in more detail, we show that his theory of Division Algorithm substantiates his structural apporaches to mathematics.

ON WEAKLY QUASI n-ABSORBING SUBMODULES

  • Issoual, Mohammed;Mahdou, Najib;Moutui, Moutu Abdou Salam
    • Bulletin of the Korean Mathematical Society
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    • v.58 no.6
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    • pp.1507-1520
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    • 2021
  • Let R be a commutative ring with 1 ≠ 0, n be a positive integer and M be an R-module. In this paper, we introduce the concept of weakly quasi n-absorbing submodule which is a proper generalization of quasi n-absorbing submodule. We define a proper submodule N of M to be a weakly quasi n-absorbing submodule if whenever a ∈ R and x ∈ M with 0 ≠ an x ∈ N, then an ∈ (N :R M) or an-1 x ∈ N. We study the basic properties of this notion and establish several characterizations.

RINGS IN WHICH EVERY IDEAL CONTAINED IN THE SET OF ZERO-DIVISORS IS A D-IDEAL

  • Anebri, Adam;Mahdou, Najib;Mimouni, Abdeslam
    • Communications of the Korean Mathematical Society
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    • v.37 no.1
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    • pp.45-56
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    • 2022
  • In this paper, we introduce and study the class of rings in which every ideal consisting entirely of zero divisors is a d-ideal, considered as a generalization of strongly duo rings. Some results including the characterization of AA-rings are given in the first section. Further, we examine the stability of these rings in localization and study the possible transfer to direct product and trivial ring extension. In addition, we define the class of dE-ideals which allows us to characterize von Neumann regular rings.

수학적 구조와 격자론

  • 홍영희
    • Journal for History of Mathematics
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    • v.15 no.2
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    • pp.175-181
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    • 2002
  • Since Noether has consolidated the structural approach to the study of algebra, the lattice theory has reemerged as a tool for the structural study for algebra and its own right as well in 1930s. We investigate the process which the mathematical structures made their foundations in Mathematics through the lattice theory in the period.

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