Some Types of Filters in Equality Algebras
Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation be...
| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
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Shahid Beheshti University
2017-07-01
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| Series: | Categories and General Algebraic Structures with Applications |
| Subjects: | |
| Online Access: | http://www.cgasa.ir/article_42342_cf5624efc3f4dd8d61c28cc7af659734.pdf |
| _version_ | 1819063339718803456 |
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| author | Rajabali Borzooei Fateme Zebardast Mona Aaly Kologani |
| author_facet | Rajabali Borzooei Fateme Zebardast Mona Aaly Kologani |
| author_sort | Rajabali Borzooei |
| collection | DOAJ |
| description | Equality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras. |
| first_indexed | 2024-12-21T15:13:06Z |
| format | Article |
| id | doaj.art-620a1a5756b5447992badee6d38216f2 |
| institution | Directory Open Access Journal |
| issn | 2345-5853 2345-5861 |
| language | English |
| last_indexed | 2024-12-21T15:13:06Z |
| publishDate | 2017-07-01 |
| publisher | Shahid Beheshti University |
| record_format | Article |
| series | Categories and General Algebraic Structures with Applications |
| spelling | doaj.art-620a1a5756b5447992badee6d38216f22022-12-21T18:59:13ZengShahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58532345-58612017-07-017Special Issue on the Occasion of Banaschewski's 90th Birthday (II)335542342Some Types of Filters in Equality AlgebrasRajabali Borzooei0Fateme Zebardast1Mona Aaly Kologani2Department of Mathematics, Shahid Beheshti University, Tehran, Iran.Department of Mathematics, Payam e Noor University, Tehran, Iran.Payam e Noor UniversityEquality algebras were introduced by S. Jenei as a possible algebraic semantic for fuzzy type theory. In this paper, we introduce some types of filters such as (positive) implicative, fantastic, Boolean, and prime filters in equality algebras and we prove some results which determine the relation between these filters. We prove that the quotient equality algebra induced by an implicative filter is a Boolean algebra, by a fantastic filter is a commutative equality algebra, and by a prime filter is a chain, under suitable conditions. Finally, we show that positive implicative, implicative, and Boolean filters are equivalent on bounded commutative equality algebras.http://www.cgasa.ir/article_42342_cf5624efc3f4dd8d61c28cc7af659734.pdfEquality algebra(positive) implicative filterfantastic filterBoolean filter |
| spellingShingle | Rajabali Borzooei Fateme Zebardast Mona Aaly Kologani Some Types of Filters in Equality Algebras Categories and General Algebraic Structures with Applications Equality algebra (positive) implicative filter fantastic filter Boolean filter |
| title | Some Types of Filters in Equality Algebras |
| title_full | Some Types of Filters in Equality Algebras |
| title_fullStr | Some Types of Filters in Equality Algebras |
| title_full_unstemmed | Some Types of Filters in Equality Algebras |
| title_short | Some Types of Filters in Equality Algebras |
| title_sort | some types of filters in equality algebras |
| topic | Equality algebra (positive) implicative filter fantastic filter Boolean filter |
| url | http://www.cgasa.ir/article_42342_cf5624efc3f4dd8d61c28cc7af659734.pdf |
| work_keys_str_mv | AT rajabaliborzooei sometypesoffiltersinequalityalgebras AT fatemezebardast sometypesoffiltersinequalityalgebras AT monaaalykologani sometypesoffiltersinequalityalgebras |