Sheffer stroke branching of BCK-algebras

Yıl 2024, Cilt: 26 Sayı: 1, 29 - 40, 19.01.2024

Tugce Katican

https://doi.org/10.25092/baunfbed.1293529

Öz

The main objective of the study is to introduce branches of Sheffer stroke BCK-algebras due their specific elements. At the onset of the study, an atom of a Sheffer stroke BCK-algebra is defined and it is shown that the set of all atoms of the algebraic structure is its subalgebra. Then it is proved that specified subsets defined by atoms of a Sheffer stroke BCK-algebra are ideals but the inverses are not true in general. Moreover, a branch and a chain on a Sheffer stroke BCK-algebra are introduced and some properties are presented. Finally, relationships between aforementioned concepts are built and supported by illustrative examples.

Anahtar Kelimeler

Sheffer stroke, Sheffer stroke BCK-algebra, ideal, atom, branch

BCK-cebirlerinin Sheffer stroke dallanması

Öz

Bu çalışmanın temel amacı, belirli elemanları yardımıyla Sheffer stroke BCK-cebirlerinin dallarını tanıtmaktır. Çalışmanın başlangıcında, bir Sheffer stroke BCK-cebirinin bir atomu tanımlanarak bu cebirsel yapının tüm atomlarının kümesinin bu yapının bir altcebiri olduğu gösterilmiştir. Ardından bir Sheffer stroke BCK-cebirinin bir atomu yardımıyla tanımlanan özel altkümelerinin bu cebirsel yapının idealleri olduğu fakat bu ifadenin tersinin genelde doğru olmadığı ispatlanmıştır. Dahası, bir Sheffer stroke BCK-cebiri üzerinde bir dal ve zincir tanımlanarak bazı özellikleri sunulmuştur. Son olarak, bahsi geçen yapılar arasındaki bağlantılar inşa edilmiştir ve bu bağlantılar açıklayıcı örneklerle desteklenmiştir.

Anahtar Kelimeler

Sheffer stroke, Sheffer stroke BCK-cebiri, ideal, atom, dal

Kaynakça

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