Steiner P-algebras

• Опубліковано в: : Algebra and Discrete Mathematics
• Дата: 2005
• Автор: Chakrabarti, S.
• Формат: Стаття
• Мова: Англійська
• Опубліковано: Інститут прикладної математики і механіки НАН України 2005
• Онлайн доступ: https://nasplib.isofts.kiev.ua/handle/123456789/156624
• 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.

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.