Characterizing finitely based abelian Mal’cev varieties

Key Points

• The aim is to characterize finitely based abelian Mal’cev varieties with specific conditions.
• Proved characterization of finitely based abelian Mal’cev varieties
• Analyzed conditions of finite type
• Assessed ring of idempotent binary terms
• Evaluated module of unary terms
• Finitely based abelian Mal’cev varieties are defined by finite type
• Ring of idempotent binary terms must be finitely presented
• Module of unary terms must also be finitely presented