The concept of a prominent interior GE-filter (of type 1 and type 2) is introduced, and their properties are investigated. The relationship between a prominent GE-filter and a prominent interior GE-filter and the relationship between an interior GE-filter and a prominent interior GE-filter are discussed. Examples to show that any interior GE-filter is not a prominent interior GE-filter and any prominent GE-filter is not a prominent interior GE-filter are provided. Conditions for an interior GE-filter to be a prominent interior GE-filter are given. Also, conditions under which an internal GE-filter larger than a given internal GE filter can become a prominent internal GE-filter are considered, and an example describing it is given. The relationship between a prominent interior GE-filter and a prominent interior GE-filter of type 1 is discussed.
Citation: Seok-Zun Song, Ravikumar Bandaru, Young Bae Jun. Prominent interior GE-filters of GE-algebras[J]. AIMS Mathematics, 2021, 6(12): 13432-13447. doi: 10.3934/math.2021778
The concept of a prominent interior GE-filter (of type 1 and type 2) is introduced, and their properties are investigated. The relationship between a prominent GE-filter and a prominent interior GE-filter and the relationship between an interior GE-filter and a prominent interior GE-filter are discussed. Examples to show that any interior GE-filter is not a prominent interior GE-filter and any prominent GE-filter is not a prominent interior GE-filter are provided. Conditions for an interior GE-filter to be a prominent interior GE-filter are given. Also, conditions under which an internal GE-filter larger than a given internal GE filter can become a prominent internal GE-filter are considered, and an example describing it is given. The relationship between a prominent interior GE-filter and a prominent interior GE-filter of type 1 is discussed.
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Seok-Zun Song, Ravikumar Bandaru, Young Bae Jun. Prominent interior GE-filters of GE-algebras[J]. AIMS Mathematics, 2021, 6(12): 13432-13447. doi: 10.3934/math.2021778
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