engleski

Pseudosquares in quadratical quasigroup

A quadratical quasigroup is defined as a quasigroup which satisfy identity $ab\cdota=ca \cdot bc$. The geometrical concept of a square and parallelogram can be defined in a general quadratical quasigroup. The concept of a skewsquare can be defined in a general quadratical quasigroup. The statements referring to to the connection between a skewsquare and geometrical concepts of the midpoint, parallelogram and a square will be obtained. The mentioned statements will be proved by means of identities and equivalencies wich hold in a general quadratical quasigroups. The geometrical representation of the obtained concepts and relations between them will be given in the quadratical quasigroup $C(1\2(1+i))$.

quadratical quasigroup ; pseudosquare

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