• 제목/요약/키워드: BCI-algebras

검색결과 84건 처리시간 0.016초

PSEUDO P-CLOSURE WITH RESPECT TO IDEALS IN PSEUDO BCI-ALGEBRAS

  • MOUSSAEI, HOSSEIN;HARIZAVI, HABIB
    • Journal of applied mathematics & informatics
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    • 제38권1_2호
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    • pp.65-77
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    • 2020

  • In this paper, for any non-empty subsets A, I of a pseudo BCI-algebra X, we introduce the concept of pseudo p-closure of A with respect to I, denoted by ApcI, and investigate some related properties. Applying this concept, we state a necessary and sufficient condition for a pseudo BCI-algebra 1) to be a p-semisimple pseudo BCI-algebra; 2) to be a pseudo BCK-algebra. Moreover, we show that Apc{0} is the least positive pseudo ideal of X containing A, and characterize it by the union of some branches. We also show that the set of all pseudo ideals of X which ApcI = A, is a complete lattice. Finally, we prove that this notion can be used to define a closure operation.

  • https://doi.org/10.14317/jami.2020.065 인용 PDF KSCI

REGULARITY OF GENERALIZED DERIVATIONS IN BCI-ALGEBRAS

  • Muhiuddin, G.
    • 대한수학회논문집
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    • 제31권2호
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    • pp.229-235
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    • 2016

  • In this paper we study the regularity of inside (or outside) (${\theta},{\phi}$)-derivations in BCI-algebras X and prove that let $d_{({\theta},{\phi})}:X{\rightarrow}X$ be an inside (${\theta},{\phi}$)-derivation of X. If there exists a ${\alpha}{\in}X$ such that $d_{({\theta},{\phi})}(x){\ast}{\theta}(a)=0$, then $d_{({\theta},{\phi})}$ is regular for all $x{\in}X$. It is also shown that if X is a BCK-algebra, then every inside (or outside) (${\theta},{\phi}$)-derivation of X is regular. Furthermore the concepts of ${\theta}$-ideal, ${\phi}$-ideal and invariant inside (or outside) (${\theta},{\phi}$)-derivations of X are introduced and their related properties are investigated. Finally we obtain the following result: If $d_{({\theta},{\phi})}:X{\rightarrow}X$ is an outside (${\theta},{\phi}$)-derivation of X, then $d_{({\theta},{\phi})}$ is regular if and only if every ${\theta}$-ideal of X is $d_{({\theta},{\phi})}$-invariant.

  • https://doi.org/10.4134/CKMS.2016.31.2.229 인용 PDF KSCI

EXISTENCE OF FUZZY IDEALS WITH ADDITIONAL CONDITIONS IN BCK/BCI-ALGEBRAS

  • Jun, Young-Bae;Park, Chul-Hwan
    • 한국수학교육학회지시리즈B:순수및응용수학
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    • 제14권3호
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    • pp.223-230
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    • 2007

  • We give an answer to the following question: Question. Let S be a subset of [0,1] containing a maximal element m > 0 and let C :=$\{I_{t}\;{\mid}\;t{\in}S\}$ be a decreasing chain of ideals of a BCK/BCI-algebra X. Then does there exists a fuzzy ideal ${\mu}(X)=S\;and\;C_{\mu}=C?$.

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