On Q-algebras
We introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH/BCI/BCK-algebras and we generalize some theorems discussed in BCI-algebras. Moreover, we introduce the notion of quadratic Q-algebra, and show that every quadratic Q-algebra (X;∗,e), e∈X, has a product of the...
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| Main Authors: | , , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2001-01-01
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| Series: | International Journal of Mathematics and Mathematical Sciences |
| Online Access: | http://dx.doi.org/10.1155/S0161171201006627 |
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| _version_ | 1832549785062604800 |
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| author | Joseph Neggers Sun Shin Ahn Hee Sik Kim |
| author_facet | Joseph Neggers Sun Shin Ahn Hee Sik Kim |
| author_sort | Joseph Neggers |
| collection | DOAJ |
| description | We introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH/BCI/BCK-algebras and we generalize some theorems discussed in BCI-algebras. Moreover, we introduce the notion of quadratic Q-algebra, and show that every quadratic Q-algebra (X;∗,e), e∈X, has a product of the form x∗y=x−y+e, where x,y∈X when X is a field with |x|≥3. |
| format | Article |
| id | doaj-art-46125c9871154150a9dd3df9dddd7e3b |
| institution | Kabale University |
| issn | 0161-1712 1687-0425 |
| language | English |
| publishDate | 2001-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | International Journal of Mathematics and Mathematical Sciences |
| spelling | doaj-art-46125c9871154150a9dd3df9dddd7e3b2025-02-03T06:08:32ZengWileyInternational Journal of Mathematics and Mathematical Sciences0161-17121687-04252001-01-01271274975710.1155/S0161171201006627On Q-algebrasJoseph Neggers0Sun Shin Ahn1Hee Sik Kim2Department of Mathematics, University of Alabama, Tuscaloosa 35487-0350, AL, USADepartment of Mathematics Education, Dongguk University, Seoul 100-715, KoreaDepartment of Mathematics, Hanyang National University, Seoul 133-791, KoreaWe introduce a new notion, called a Q-algebra, which is a generalization of the idea of BCH/BCI/BCK-algebras and we generalize some theorems discussed in BCI-algebras. Moreover, we introduce the notion of quadratic Q-algebra, and show that every quadratic Q-algebra (X;∗,e), e∈X, has a product of the form x∗y=x−y+e, where x,y∈X when X is a field with |x|≥3.http://dx.doi.org/10.1155/S0161171201006627 |
| spellingShingle | Joseph Neggers Sun Shin Ahn Hee Sik Kim On Q-algebras International Journal of Mathematics and Mathematical Sciences |
| title | On Q-algebras |
| title_full | On Q-algebras |
| title_fullStr | On Q-algebras |
| title_full_unstemmed | On Q-algebras |
| title_short | On Q-algebras |
| title_sort | on q algebras |
| url | http://dx.doi.org/10.1155/S0161171201006627 |
| work_keys_str_mv | AT josephneggers onqalgebras AT sunshinahn onqalgebras AT heesikkim onqalgebras |