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SQS-3-Groupoid with q(x,x,y)=x
Authors: M. H. Armanious
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Abstract
A new algebraic structure (P; q) of a Steiner quadruple systems SQS (P;B) called an SQS-3-groupoid with q(x; x; y) = x (briefly: an SQS-3-quasigroup) is defined and some of its properties are described. Sloops are considered as derived algebras of SQS-skeins. Squags and also commutative loops of exponent 3 with x(xy)^2 = y^2 given in [7] are derived algebras of SQS-3-groupoids. The role of SQS-3-groupoids in the clarification of the connections between squags and commutative loops of exponent 3 is described.M. H. Armanious
Department of Mathematics,
Faculty of Science,
Mansoura University,
Mansoura,
Egypt.
E-mail:
Department of Mathematics,
Faculty of Science,
Mansoura University,
Mansoura,
Egypt.
E-mail:
Fulltext
– 0.42 Mb
Contents
- SQS-3-Groupoid with q(x,x,y)=x
- Some results on hyper BCK-algebras
- Quasi p-ideals of quasi BCI-algebras
- On groupoids with identity x(xy) = y
- m-systems and n-systems in ordered semigroups
- Fuzzy congruences on groups
- Quotient groups induced by fuzzy subgroups
- Zeroids and idempoids in AG-groupoids
- Characterization of division µ-LA-semigroups
- A note on Salem numbers and Golden mean
- Abel-Grassmann\'s bands
- Hyper I-algebras and polygroups
- Extensions of Latin subsquares and local embeddability of groups and group algebras
