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) = der_𝜃,b(G,⋅) is equational noetherian, if and only if the ordinary group (G,⋅) is equational noetherian. The structure of coordinate polyadic group of algebraic sets in equational noetherian polyadic groups is also determined.

KEYWORDS:

• Algebraic sets
• coordinate polyadic groups
• equational noetherian property
• equations
• free polyadic groups
• n-ary groups
• polyadic groups
• post’s cover
• universal algebraic geometry

2010 MATHEMATICS SUBJECT CLASSIFICATION:

• Primary: 20N15
• Secondary: 08A99
• 14A99