Про звідність функційних рівнянь функційної довжини 6

• Date: 2020
• Main Author: Krainichuk, H. V.; Крайнічук Г. В.; Донецький національний університет ім. Василя Стуса, Вінниця
• Format: Article
• Language: Ukrainian
• Published: Pidstryhach Institute for Applied Problems of Mechanics and Mathematics of NAS of Ukraine 2020
• Subjects: квазігрупа; функційне рівняння; тотожність; парастрофно-первин­на рівносильність; медіальність; псевдомедіальність; звідність; скорот­ність
• Online Access: http://journals.iapmm.lviv.ua/ojs/index.php/APMM/article/view/apmm2020.18.102-110
• Journal Title: Prykladni Problemy Mekhaniky i Matematyky

The article analyzes the results of generalized quadratic functional equations of functional length six on a set of binary quasigroups with respect to definitions of cancellability known in the literature. Different definitions of cancellability are called cancellability of type a, b, c. It is proved that the functional equation of generalized pseudomediality is uncancellable of type a and type c, but cancellable of type b, and therefore reducible. It is established that the generalized pseudomediality is equivalent to the system of equations from a smaller number of variables. It is found a reducible equation which is parastrophically primary equivalent to the equation of generalized mediality. Therefore, the generalized mediality is parastrophically reducible, although it is uncancellable in three types. The classification of uncancellable type b equations of length 6 has been clarified. It is established that uncancellable type b equations of length 6 are reducible. It is proved that all quadratic equations of functional length 6 are reducible.  Cite as: H. V. Krainichuk, “On the reducibility of functional equations of functional length 6,” Prykl. Probl. Mekh. Mat., Issue 18, 102–110 (2020) (in Ukrainian), https://doi.org/10.15407/apmm2020.18.102-110