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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| Veröffentlicht in: | Algebra and Discrete Mathematics |
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| Datum: | 2005 |
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| Format: | Artikel |
| Sprache: | English |
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Інститут прикладної математики і механіки НАН України
2005
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| Online Zugang: | https://nasplib.isofts.kiev.ua/handle/123456789/156624 |
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| Назва журналу: | Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| Zitieren: | Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ. |
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Chakrabarti, S. 2019-06-18T17:56:34Z 2019-06-18T17:56:34Z 2005 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. https://nasplib.isofts.kiev.ua/handle/123456789/156624 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. Author is grateful to Dr.P.K.Saxena; Director, SAG, DRDO for his permission and constant encouragement for the research. My heartiest thanks to Dr.R.K.Khanna; Scientist ’E’, SAG for valuable discussions and constant inspiration throughout this research work. Author also expressed her heartiest gratitude to Prof V.A.Artamonov for his valuable comments for the improvements of the paper. en Інститут прикладної математики і механіки НАН України Algebra and Discrete Mathematics Steiner P-algebras Article published earlier |
| institution |
Digital Library of Periodicals of National Academy of Sciences of Ukraine |
| collection |
DSpace DC |
| title |
Steiner P-algebras |
| spellingShingle |
Steiner P-algebras Chakrabarti, S. |
| 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 |
| author |
Chakrabarti, S. |
| author_facet |
Chakrabarti, S. |
| publishDate |
2005 |
| language |
English |
| container_title |
Algebra and Discrete Mathematics |
| publisher |
Інститут прикладної математики і механіки НАН України |
| format |
Article |
| 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.
|
| issn |
1726-3255 |
| url |
https://nasplib.isofts.kiev.ua/handle/123456789/156624 |
| fulltext |
|
| citation_txt |
Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ. |
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AT chakrabartis steinerpalgebras |
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2025-11-24T15:19:05Z |
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2025-11-24T15:19:05Z |
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1850847950136147969 |