Steiner P-algebras
General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them. It has lots of applications in theoretical computer science, secure communications etc. Combinatorial designs play significa...
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| Видавець: | Інститут прикладної математики і механіки НАН України |
|---|---|
| Дата: | 2005 |
| Автор: | |
| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Інститут прикладної математики і механіки НАН України
2005
|
| Назва видання: | Algebra and Discrete Mathematics |
| Онлайн доступ: | http://dspace.nbuv.gov.ua/handle/123456789/156624 |
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| Цитувати: | Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ. |
Репозиторії
Digital Library of Periodicals of National Academy of Sciences of Ukraine| id |
irk-123456789-156624 |
|---|---|
| record_format |
dspace |
| spelling |
irk-123456789-1566242019-06-19T01:29:13Z Steiner P-algebras Chakrabarti, S. General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them. It has lots of applications in theoretical computer science, secure communications etc. Combinatorial designs play significant role in these areas. Steiner Triple Systems (STS) which are particular case of Balanced Incomplete Block Designs (BIBD) from combinatorics can be regarded as algebraic systems. Steiner quasigroups (Squags) and Steiner loops (Sloops) are two well known algebraic systems which are connected to STS. There is a one-to-one correspondence between STS and finite Squags and finite Sloops. A new algebraic system w.r.to a ternary operation P based on a Steiner Triple System introduced in [3]. In this paper the abstraction and the generalization of the properties of the ternary operation defined in [3] has been made. A new class of algebraic systems Steiner P-algebras has been introduced. The one-to-one correspondence between STS on a linearly ordered set and finite Steiner P-algebras has been established. Some identities have been proved. 2005 Article Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ. 1726-3255 2000 Mathematics Subject Classification: 08A62. http://dspace.nbuv.gov.ua/handle/123456789/156624 en Algebra and Discrete Mathematics Інститут прикладної математики і механіки НАН України |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| language |
English |
| description |
General algebraic systems are able to formalize problems of different branches of mathematics from the algebraic point of view by establishing the connectivity between them.
It has lots of applications in theoretical computer science, secure
communications etc. Combinatorial designs play significant role
in these areas. Steiner Triple Systems (STS) which are particular
case of Balanced Incomplete Block Designs (BIBD) from combinatorics can be regarded as algebraic systems. Steiner quasigroups
(Squags) and Steiner loops (Sloops) are two well known algebraic
systems which are connected to STS. There is a one-to-one correspondence between STS and finite Squags and finite Sloops. A new
algebraic system w.r.to a ternary operation P based on a Steiner
Triple System introduced in [3].
In this paper the abstraction and the generalization of the properties of the ternary operation defined in [3] has been made. A new
class of algebraic systems Steiner P-algebras has been introduced.
The one-to-one correspondence between STS on a linearly ordered
set and finite Steiner P-algebras has been established. Some identities have been proved. |
| format |
Article |
| author |
Chakrabarti, S. |
| spellingShingle |
Chakrabarti, S. Steiner P-algebras Algebra and Discrete Mathematics |
| author_facet |
Chakrabarti, S. |
| author_sort |
Chakrabarti, S. |
| title |
Steiner P-algebras |
| title_short |
Steiner P-algebras |
| title_full |
Steiner P-algebras |
| title_fullStr |
Steiner P-algebras |
| title_full_unstemmed |
Steiner P-algebras |
| title_sort |
steiner p-algebras |
| publisher |
Інститут прикладної математики і механіки НАН України |
| publishDate |
2005 |
| url |
http://dspace.nbuv.gov.ua/handle/123456789/156624 |
| citation_txt |
Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ. |
| series |
Algebra and Discrete Mathematics |
| work_keys_str_mv |
AT chakrabartis steinerpalgebras |
| first_indexed |
2023-05-20T17:50:18Z |
| last_indexed |
2023-05-20T17:50:18Z |
| _version_ |
1796154201885114368 |