1,722,208 research outputs found
Deductive systems of BCK-algebras
No full textsummary:In this paper we shall give some results on irreducible deductive systems in BCK-algebras and we shall prove that the set of all deductive systems of a BCK-algebra is a Heyting algebra. As a consequence of this result we shall show that the annihilator of a deductive system is the the pseudocomplement of . These results are more general than that the similar results given by M. Kondo in [7]
SEMI-HOMOMORFISMA BCK-ALJABAR
No full textSuatu BCK-aljabar merupakan kelas dari K-aljabar bilamana grup pembangunnya adalah grup komutatif, sehingga sifat-sifat yang berlaku pada K-aljabar akan berlaku juga pada BCK-aljabar. Jika pada grup terdapat konsep homomorfisma grup, maka pada BCK-aljabar juga terdapat homomorfisma BCK-aljabar. Selain homomorfisma BCK-aljabar juga terdapat ideal dari BCK-aljabar. Sebagai generalisasi dari homomorfisma BCK-aljabar, akan diperkenalkan semi-homomorfisma BCK-aljabar. Dapat diperlihatkan setiap homomorfisma BCK-aljabar adalah semi-homomorfisma BCK-aljabar. Akan tetapi dengan memanfaatkan konsep ideal dari BCK-aljabar dapat dibuktikan semi-homomorfisma BCK-aljabar merupakan homomorfisma BCK-aljabar
Fuzzy implicative hyper BCK-ideals of hyper BCK-algebras
No full textWe consider the fuzzification of the notion of implicative hyper
BCK-ideals, and then investigate several properties.
Using the concept of level subsets, we give a
characterization of a fuzzy implicative hyper BCK-ideal. We state
a relation between a fuzzy hyper BCK-ideal and a fuzzy implicative
hyper BCK-ideal. We establish a condition for a fuzzy hyper
BCK-ideal to be a fuzzy implicative hyper BCK-ideal. Finally, we
introduce the notion of hyper homomorphisms of hyper
BCK-algebras, and discuss related properties
Mengkonstruksi Quotient BCK-aljabar dengan Fuzzy BCK-Filter
No full textPada skripsi ini akan dibuktikan beberapa teorema dari BCK-aljabar dan fuzzy BCK-filter. BCK-aljabar didefinisikan sebagai himpunan tidak kosong X dengan suatu operasi biner ∗ dan konstanta . BCK-aljabar yang memiliki elemen satuan disebut terbatas. Pada BCK-aljabar yang bersifat terbatas, dapat didefinisikan pengertian dari fuzzy BCK-filter. Selanjutnya akan dikonstruksi suatu quotient BCK-aljabar dengan fuzzy BCK-filter
Annihilators in BCK-algebras
No full textsummary:We introduce the concepts of an annihilator and a relative annihilator of a given subset of a BCK-algebra . We prove that annihilators of deductive systems of BCK-algebras are again deductive systems and moreover pseudocomplements in the lattice of all deductive systems on . Moreover, relative annihilators of with respect to are introduced and serve as relative pseudocomplements of w.r.t. in
BCK-Aljabar Hiper
No full textSuatu BCK-aljabar hiper dapat dipandang sebagai BCK-aljabar dimana peran operasi biner yang berlaku pada BCK-aljabar diambil alih oleh operasi hiper yang berlaku pada BCK-aljabar hiper. Kemudian karena operasi hiper merupakan pemetaan dari himpunan ke keluarga himpunan sehingga operasi hiper yang berlaku pada BCK-aljabar hiper merupakan perumuman dari operasi biner yang berlaku pada BCK-aljabar. Karena BCK-aljabar hiper dapat dipandang sebagai BCK-aljabar sehingga sifat-sifat yang berlaku pada BCK-aljabar juga berlaku pada BCK-aljabar hiper. Dengan menggunakan sifat-sifat yang berlaku pada BCK-aljabar, akan dibuktikan sifat-sifat yang berlaku pada BCK-aljabar hiper. Kemudian diberikan juga relasi yang lebih khusus yang berlaku pada BCK-aljabar hiper yang dinamakan relasi hiper
Semi-homomorfisma Bck-aljabar
No full textA BCK-algebra is one of the algebraic structure generated over an abelian group. So that, some concepts in group also can be found this structure, for instance, if at a group we have a homomorphism, then at the BCK-algebras we also have a homomorphism, exactly a homomorphism of BCK-algebras. In this paper we discussed a semi-homomorphism of BCK-algebara as generalization of a homomorphism of BCK-algebras. It can be shown every homomorphism of BCK-algebras is a semi-homomorphism of BCK-algebras, conversely not true. By utilizing concept of ideal of BCK-algebras can be proved a semi-homomorphism of BCK-algebras is a homomorphism of BCK-algebras
NEUTRO-BCK-ALGEBRA
No full textThis paper introduces the novel concept of Neutro-BCK-algebra. In Neutro-BCK-algebra, the outcome of any given two elements under an underlying operation (neutro-sophication procedure) has three cases, such as: appurtenance, non-appurtenance, or indeterminate. While for an axiom: equal, non-equal, or indeterminate. This study investigates the Neutro-BCK-algebra and shows that Neutro-BCK-algebra are different from BCK-algebra. The notation of Neutro-BCK-algebra generates a new concept of NeutroPoset and Neutro-Hass-diagram for NeutroPosets. Finally, we consider an instance of applications of the Neutro-BCK-algebra
On BCK, BCI-Algebra
No full text본 연구에서는 수학적 구조 가운데서 대수적 구조의 한 분야인 BCK-대수와 BCI-대수에 대하여 다음 사항들을 알아보았다.
(1) BCK-대수를 소개하고 몇 가지 예를 들었다.
(2) BCK-대수의 성질 가운데서 ideal, implicative ideal, Kernel에 관한 간단한 성질들을 증명하여 보았다.
(3) BCK-대수 사이의 homomorphism을 살피고 이것에서 유도되는 정리들을 증명하여 보았다.
(4) BCI-대수를 소개하고 몇 가지 예를 들었다.
(5) BCI-대수의 성질 가운데에서 포함관계, (x * y) * z = (x * z) * y 및 간단한 성질들을 증명하여 보았다.
(6) BCK-대수와 BCI-대수의 관계를 알아보고 이 정리들을 증명하여 보았다.;In this paper, we study following items of BCK, BCI-algebra, a field of algebra structures.
1) BCK-algebra and some examples.
2) The nature of BCK-algebra with viewpoint of ideal, implicative ideal, kernel and other some simple properties.
3) Homomorphism of BCK-algebra and several theorems derived from it.
4) BCI-algebra and some examples.
5) The nature of BCI-algebra with viewpoint of inclusion, (x * y) * z = (x * z) * y and other some simple properties
6) The relationship between BCK, BCI-algebra and those theorems.논문개요 = ⅳ
Ⅰ. 서론 = 1
Ⅱ. BCK-대수의 정의와 예 = 5
Ⅲ. BCK-대수의 성질 = 12
Ⅳ. BCK-대수의 정리 = 14
Ⅴ. BCI-대수의 정의와 예 = 24
Ⅵ. BCI-대수의 성질 = 29
Ⅶ. BCK-대수와 BCI-대수의 관계 = 33
참고문헌 = 40
ABSTRACT = 4
Weakly Injective BCK-Modules
No full textWe introduce the notion of weakly injective BCK-module and show that Baer's criterion holds for weakly injective BCK-modules but not for injective BCK-modules in general. We also provide examples and counterexamples of weakly injective BCK-modules.</jats:p
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