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 significant...
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| Видавець: | Lugansk National Taras Shevchenko University |
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| Дата: | 2018 |
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| Формат: | Стаття |
| Мова: | English |
| Опубліковано: |
Lugansk National Taras Shevchenko University
2018
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| Онлайн доступ: | https://admjournal.luguniv.edu.ua/index.php/adm/article/view/934 |
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Algebra and Discrete Mathematics| id |
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oai:ojs.admjournal.luguniv.edu.ua:article-9342018-03-21T06:34:59Z Steiner \(P\)-algebras Chakrabarti, Sucheta Balanced incomplete block designs, Steiner triple systems, General algebraic structures, Steiner quasigroup, Steiner loop, Steiner \(P\)-algebra 08A62 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. Lugansk National Taras Shevchenko University 2018-03-21 Article Article Peer-reviewed Article application/pdf https://admjournal.luguniv.edu.ua/index.php/adm/article/view/934 Algebra and Discrete Mathematics; Vol 4, No 2 (2005) 2415-721X 1726-3255 en https://admjournal.luguniv.edu.ua/index.php/adm/article/view/934/463 Copyright (c) 2018 Algebra and Discrete Mathematics |
| institution |
Algebra and Discrete Mathematics |
| collection |
OJS |
| language |
English |
| topic |
Balanced incomplete block designs Steiner triple systems General algebraic structures Steiner quasigroup Steiner loop Steiner \(P\)-algebra 08A62 |
| spellingShingle |
Balanced incomplete block designs Steiner triple systems General algebraic structures Steiner quasigroup Steiner loop Steiner \(P\)-algebra 08A62 Chakrabarti, Sucheta Steiner \(P\)-algebras |
| topic_facet |
Balanced incomplete block designs Steiner triple systems General algebraic structures Steiner quasigroup Steiner loop Steiner \(P\)-algebra 08A62 |
| format |
Article |
| author |
Chakrabarti, Sucheta |
| author_facet |
Chakrabarti, Sucheta |
| author_sort |
Chakrabarti, Sucheta |
| 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 |
| 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. |
| publisher |
Lugansk National Taras Shevchenko University |
| publishDate |
2018 |
| url |
https://admjournal.luguniv.edu.ua/index.php/adm/article/view/934 |
| work_keys_str_mv |
AT chakrabartisucheta steinerpalgebras |
| first_indexed |
2024-04-12T06:27:46Z |
| last_indexed |
2024-04-12T06:27:46Z |
| _version_ |
1796109256254029824 |