Sheffer stroke branching of BCK-algebras

Tugce Katican

Article Details

Sheffer stroke branching of BCK-algebras

Authors:

Tugce Katican

Publisher:

Balıkesir University

Main Topics:

Cebir ve Sayı Teorisi

Journal:

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.26 Issue 1, pp.29-40

Document Type:

Article

Publication Date:

1/2024

Document Language:

English

Document ID (Org No.):

2001303635

pISSN:

1301-7985

Keywords:

Abstract:

 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.

 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.

 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.

 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.

Article Details

Sheffer stroke branching of BCK-algebras

Authors:

Tugce Katican

Publisher:

Balıkesir University

Main Topics:

Cebir ve Sayı Teorisi

Journal:

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.26 Issue 1, pp.29-40

Document Type:

Article

Publication Date:

1/2024

Document Language:

English

Document ID (Org No.):

2001303635

pISSN:

1301-7985

Sheffer stroke

Sheffer stroke BCK-algebra

ideal

atom

branchSheffer stroke

Sheffer stroke BCK-cebiri

ideal

atom

dal

Issues

Article Details

Authors: Tugce Katican

Publisher: Balıkesir University

Main Topics: Cebir ve Sayı Teorisi

Journal: Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.26 Issue 1, pp.29-40

Document Type: Article

Publication Date: 1/2024

Document Language: English

Document ID (Org No.): 2001303635

pISSN: 1301-7985

Issues

Authors:

Tugce Katican

Publisher:

Balıkesir University

Main Topics:

Cebir ve Sayı Teorisi

Journal:

Balıkesir Üniversitesi Fen Bilimleri Enstitüsü Dergisi Vol.26 Issue 1, pp.29-40

Document Type:

Article

Publication Date:

1/2024

Document Language:

English

Document ID (Org No.):

2001303635

pISSN:

1301-7985