Extension of stabilizers on subtraction algebras
This paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The...
Saved in:
| Main Authors: | , |
|---|---|
| Format: | Article |
| Language: | English |
| Published: |
Shahid Bahonar University of Kerman
2024-12-01
|
| Series: | Journal of Mahani Mathematical Research |
| Subjects: | |
| Online Access: | https://jmmrc.uk.ac.ir/article_4449_ffb04dd414f13c1ca57c35fb7165be69.pdf |
| Tags: |
Add Tag
No Tags, Be the first to tag this record!
|
| _version_ | 1841560217588858880 |
|---|---|
| author | Saeide Zahiri Farshad Nahangi |
| author_facet | Saeide Zahiri Farshad Nahangi |
| author_sort | Saeide Zahiri |
| collection | DOAJ |
| description | This paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The study reveals that both the stabilizer of a subset and the stabilizer of an ideal with respect to another ideal are, in fact, ideals themselves. Investigating the impact of stabilizers on product and quotient subtraction algebras is a focal point. Additionally, a novel concept termed the ”stabilizer operation” is defined, and it is proven that the collection of ideals endowed with a binary stabilizer operator forms a bounded Hilbert algebra. |
| format | Article |
| id | doaj-art-c8f81b74d6b541f1890225babee30e6e |
| institution | Kabale University |
| issn | 2251-7952 2645-4505 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Shahid Bahonar University of Kerman |
| record_format | Article |
| series | Journal of Mahani Mathematical Research |
| spelling | doaj-art-c8f81b74d6b541f1890225babee30e6e2025-01-04T19:29:50ZengShahid Bahonar University of KermanJournal of Mahani Mathematical Research2251-79522645-45052024-12-0113416517910.22103/jmmr.2024.23142.15994449Extension of stabilizers on subtraction algebrasSaeide Zahiri0Farshad Nahangi1Department of Mathematics, Faculty of Science, Higher Education Center of Eghlid, Eghlid, IranASU School of Computing and Augmented Intelligence, Tempe, AZ, USAThis paper explores the intersection between the class of bounded subtraction algebras and the class of Boolean algebras, demonstrating their equivalence. It introduces the concepts of stabilizers for subsets and the stabilizers of one subset with respect to another within subtraction algebras. The study reveals that both the stabilizer of a subset and the stabilizer of an ideal with respect to another ideal are, in fact, ideals themselves. Investigating the impact of stabilizers on product and quotient subtraction algebras is a focal point. Additionally, a novel concept termed the ”stabilizer operation” is defined, and it is proven that the collection of ideals endowed with a binary stabilizer operator forms a bounded Hilbert algebra.https://jmmrc.uk.ac.ir/article_4449_ffb04dd414f13c1ca57c35fb7165be69.pdf(bounded) subtraction algebrastabilizerhilbert algebra |
| spellingShingle | Saeide Zahiri Farshad Nahangi Extension of stabilizers on subtraction algebras Journal of Mahani Mathematical Research (bounded) subtraction algebra stabilizer hilbert algebra |
| title | Extension of stabilizers on subtraction algebras |
| title_full | Extension of stabilizers on subtraction algebras |
| title_fullStr | Extension of stabilizers on subtraction algebras |
| title_full_unstemmed | Extension of stabilizers on subtraction algebras |
| title_short | Extension of stabilizers on subtraction algebras |
| title_sort | extension of stabilizers on subtraction algebras |
| topic | (bounded) subtraction algebra stabilizer hilbert algebra |
| url | https://jmmrc.uk.ac.ir/article_4449_ffb04dd414f13c1ca57c35fb7165be69.pdf |
| work_keys_str_mv | AT saeidezahiri extensionofstabilizersonsubtractionalgebras AT farshadnahangi extensionofstabilizersonsubtractionalgebras |