${\mathcal N}$-subalgebras of type $(\in, \in \! \vee \, {\rm q})$ based on point ${\mathcal N}$-structures in $BCK/BCI$-algebras
Commun. Korean Math. Soc. 2012 Vol. 27, No. 3, 431-439
https://doi.org/10.4134/CKMS.2012.27.3.431
Printed September 1, 2012
Kyoung Ja Lee, Young Bae Jun, and Xiaohong Zhang
Hannam University, Gyeongsang National University, Shanghai Maritime University
Abstract : Characterizations of ${\mathcal N}$-subalgebra of type $(\in, \in \vee q)$ are provided. The notion of ${\mathcal N}$-subalgebras of type $(\overline{\in}, \overline{\in} \vee \overline{q})$ is introduced, and its characterizations are discussed. Conditions for an ${\mathcal N}$-subalgebra of type $(\in, \in \vee q)$ (resp. $(\overline{\in}, \overline{\in} \vee \overline{q})$) to be an ${\mathcal N}$-subalgebra of type $(\in, \in)$ are considered.
Keywords : point ${\mathcal N}$-structure, closed (resp. open) support, $q$-support, $\in \! \vee {q}$-support, ${\mathcal N}$-subalgebra of types $(\in, \in \vee q)$, $(\overline{\in}, \overline{\in} \vee \overline{q})$
MSC numbers : 06F35, 03G25
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