Communications of the
Korean Mathematical Society CKMS

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