Malaysian Journal of Mathematical Sciences, September 2023, Vol. 17, No. 3
Extended Filters of $\textit{MS}$-Algebras
Gaber, A., Seoud, M. A., and Tarek, M.
Corresponding Email: Mona.Saad@sci.asu.edu.eg
Received date: 31 May 2023
Accepted date: 21 August 2023
Abstract:
For a filter $T$ of an $\textit{MS}$-algebra $\mathfrak{L}$ and a subset $Z$ of $\mathfrak{L}$, a new extension filter of $T$ is introduced, denoted by $E_T(Z)$. Many properties of $E_T(Z)$ are investigated and the lattice structure of the set of all $E_T(Z)$ is studied. A new definition related to $E_T(Z)$ is presented, called fixed filters relative to a subset of $\mathfrak{L}$. A generalisation of $E_T(Z)$ is illustrated by introducing the concept of strong filters, notated by $\overline{E_T(Z)}$. The strong extension $\overline{E_T(Z)}$ is characterized by the intersection of all strong filters fixed relative to an ideal $\mathfrak{L}-\mathfrak{P}$ for a prime filter $\mathfrak{P}$ of $\mathfrak{L}$.
Keywords: ounded distributive lattice; $\textit{MS}$-algebra; filter; ideal
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