Equations in polyadic groups

Abstract

Systems of equations and their solution sets are studied in polyadic groups. We prove that a polyadic group $(G,f)={\mathrm{der}}_{\theta ,b}(G,\cdot )$ is equational noetherian, if and only if the ordinary group $(G,\cdot )$ is equational noetherian. The structure of coordinate polyadic group of algebraic sets in equational noetherian polyadic groups are also determined.

15 pages

References in corpus (2)

• Around the Hosszú-Gluskin theorem for $n$-ary groups
• Algebraic geometry over algebraic structures III: Equationally Noetherian property and compactness

Cited by in corpus (1)

• Lectures notes in universal algebraic geometry