On the Classification of Bol-Moufang Type of Some Varieties of Quasi Neutrosophic Triplet Loop (Fenyves BCI-Algebras)
| Autor: | Emmanuel Ilojide, Memudu Olaposi Olatinwo, Tèmítọ́pẹ́ Gbọ́láhàn Jaíyéọlá, Florentin Smarandache |
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| Jazyk: | angličtina |
| Rok vydání: | 2018 |
| Předmět: |
Pure mathematics
Physics and Astronomy (miscellaneous) Algebraic structure lcsh:Mathematics General Mathematics 010102 general mathematics loop 02 engineering and technology Type (model theory) lcsh:QA1-939 quasigroup 01 natural sciences Fenyves identities Loop (topology) quasi neutrosophic loops Bol-Moufang Chemistry (miscellaneous) 0202 electrical engineering electronic engineering information engineering Computer Science (miscellaneous) 020201 artificial intelligence & image processing BCI-algebra 0101 mathematics Quasigroup Associative property Mathematics |
| Zdroj: | Symmetry Volume 10 Issue 10 Pages: 427 Symmetry, Vol 10, Iss 10, p 427 (2018) |
| ISSN: | 2073-8994 |
| DOI: | 10.3390/sym10100427 |
| Popis: | In this paper, Bol-Moufang types of a particular quasi neutrosophic triplet loop (BCI-algebra), chritened Fenyves BCI-algebras are introduced and studied. 60 Fenyves BCI-algebras are introduced and classified. Amongst these 60 classes of algebras, 46 are found to be associative and 14 are found to be non-associative. The 46 associative algebras are shown to be Boolean groups. Moreover, necessary and sufficient conditions for 13 non-associative algebras to be associative are also obtained: p-semisimplicity is found to be necessary and sufficient for a F 3 , F 5 , F 42 and F 55 algebras to be associative while quasi-associativity is found to be necessary and sufficient for F 19 , F 52 , F 56 and F 59 algebras to be associative. Two pairs of the 14 non-associative algebras are found to be equivalent to associativity ( F 52 and F 55 , and F 55 and F 59 ). Every BCI-algebra is naturally an F 54 BCI-algebra. The work is concluded with recommendations based on comparison between the behaviour of identities of Bol-Moufang (Fenyves’ identities) in quasigroups and loops and their behaviour in BCI-algebra. It is concluded that results of this work are an initiation into the study of the classification of finite Fenyves’ quasi neutrosophic triplet loops (FQNTLs) just like various types of finite loops have been classified. This research work has opened a new area of research finding in BCI-algebras, vis-a-vis the emergence of 540 varieties of Bol-Moufang type quasi neutrosophic triplet loops. A ‘Cycle of Algebraic Structures’ which portrays this fact is provided. |
| Databáze: | OpenAIRE |
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