Imploring interior GE-filters in GE-algebras

Sun Shin Ahn; Ravikumar Bandaru; Young Bae Jun; Sun Shin Ahn; Ravikumar Bandaru; Young Bae Jun

doi:10.3934/math.2022051

AIMS Mathematics

2022, Volume 7, Issue 1: 855-868. doi: 10.3934/math.2022051

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Imploring interior GE-filters in GE-algebras

1.
Department of Mathematics Education, Dongguk University, Seoul 04620, Korea
2.
Department of Mathematics, GITAM (Deemed to be University), Hyderabad Campus, Telangana-502329, India
3.
Department of Mathematics Education, Gyeongsang National University, Jinju 52828, Korea

Received: 20 May 2021 Accepted: 13 October 2021 Published: 18 October 2021
MSC : 03G25, 06F35

The concept of an imploring interior GE-filter is introduced, and their properties are investigated. The relationship between an interior GE-filter and an imploring interior GE-filter are discussed. Example to show that any interior GE-filter is not an imploring interior GE-filter is provided. Conditions for an interior GE-filter to be an imploring interior GE-filter are given. Examples to show that an imploring interior GE-filter is independent to a belligerent interior GE-filter are provided. Conditions for an imploring interior GE-filter to be a belligerent interior GE-filter are given. The relationship between imploring interior GE-filter and prominent interior GE-filter are discussed. Example to show that any imploring interior GE-filter is not a prominent interior GE-filter is provided. Conditions for an imploring interior GE-filter to be a prominent interior GE-filter are given. Also, conditions under which an interior GE-filter larger than a given interior GE-filter can become an imploring interior GE-filter are considered.
- (pre-transitive) GE-algebra,
- GE-filter,
- interior GE-filter,
- imploring interior GE-filter,
- prominent interior GE-filter
Citation: Sun Shin Ahn, Ravikumar Bandaru, Young Bae Jun. Imploring interior GE-filters in GE-algebras[J]. AIMS Mathematics, 2022, 7(1): 855-868. doi: 10.3934/math.2022051

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Abstract

The concept of an imploring interior GE-filter is introduced, and their properties are investigated. The relationship between an interior GE-filter and an imploring interior GE-filter are discussed. Example to show that any interior GE-filter is not an imploring interior GE-filter is provided. Conditions for an interior GE-filter to be an imploring interior GE-filter are given. Examples to show that an imploring interior GE-filter is independent to a belligerent interior GE-filter are provided. Conditions for an imploring interior GE-filter to be a belligerent interior GE-filter are given. The relationship between imploring interior GE-filter and prominent interior GE-filter are discussed. Example to show that any imploring interior GE-filter is not a prominent interior GE-filter is provided. Conditions for an imploring interior GE-filter to be a prominent interior GE-filter are given. Also, conditions under which an interior GE-filter larger than a given interior GE-filter can become an imploring interior GE-filter are considered.

References

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