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On BF-algebras

Title
On BF-algebras
Other Titles
BF-ALGEBRAS에 관하여
Author
계나리
Alternative Author(s)
계나리
Advisor(s)
김희식
Issue Date
2007-02
Publisher
한양대학교
Degree
Master
Abstract
본 논문에서는 BF-대수에서 정규 이데알과 닫힌 이데알의 성질을 알아보고, 이데알이 적당한 집합의 합집합으로 분해되며, 집합 I^(0)가 가장 큰 닫힌 이데알임을 보인다. 그리고 quadratic BF-대수의 개념을 소개하고, 집합의 크기가 3보다 큰 체에서 BG/Q/B-대수와 동치가 됨을 보인다. 마지막으로 BF-대수에서 여러 동형사상에 관해 살펴본다.; In this thesis, we study some properties of(normal, closed) ideals in BF-algebras, especially we show that any ideal of BF-algebra can be decomposed into the union of some sets, and obtain the greatest closed ideal I0 of an ideal I of a BF-algebra X contained in I. And we introduced the notion of a quadratic BF-algebra, and obtain the quadratic BF-algebras, BG-algebras, quadratic Q-algebras, and quadratic B-algebras are equivalent notions on a field X with |X|>3, and hence every quadratic BF-algebra is a BCI-algebra. Moreover, we discuss some fundamental theorem of homomorphisms for BF-algebras.
URI
https://repository.hanyang.ac.kr/handle/20.500.11754/150144http://hanyang.dcollection.net/common/orgView/200000405488
Appears in Collections:
GRADUATE SCHOOL[S](대학원) > MATHEMATICS(수학과) > Theses (Master)
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