Positive implicative True-False ideals in BCK-algebras

Document Type : Research Paper

Authors

1 Department of Mathematics, Faculty of Mathematical Sciences, Shahid Beheshti University, Tehran, Iran

2 Department of Mathematics Education, Gyeongsang National University, Chinju 660-701, Republic of Korea

3 Hatef Higher Education Institute, Zahedan, Iran

Abstract

In BCK-algebra, the concept of  a positive implicative $T\&F$-ideal is introduced, and further several properties are  investigated. The relationship between  $T\&F$-ideals and  positive implicative $T\&F$-ideals is established, and an example is given to reveal that  a $T\&F$-ideal is not a positive implicative $T\&F$-ideal. Various conditions under which  a $T\&F$-ideal can be a positive implicative $T\&F$-ideal are explored and various characterizations of a positive  implicative $T\&F$-ideal are studied. The extended property of a positive implicative $T\&F$-ideal is constructed.

Keywords

References

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Journal of Mahani Mathematical Research
Volume 11, Issue 3 - Serial Number 23
Special Issue dedicated to Prof. Mashaallah Mashinchi.
November 2022
Pages 69-85

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History

  • Receive Date: 07 March 2022
  • Revise Date: 04 May 2022
  • Accept Date: 30 May 2022

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