Steiner P-algebras

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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Бібліографічні деталі
Дата:2005
Автор: Chakrabarti, S.
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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Назва журналу:Digital Library of Periodicals of National Academy of Sciences of Ukraine
Цитувати:Steiner P-algebras / S. Chakrabarti // Algebra and Discrete Mathematics. — 2005. — Vol. 4, № 2. — С. 36–45. — Бібліогр.: 4 назв. — англ.

Репозитарії

Digital Library of Periodicals of National Academy of Sciences of Ukraine
id irk-123456789-156624
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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
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