Some New Results on N(2,2,0)-Algebras

An N(2,2,0)-algebra (abbreviated as NA-algebra) is an algebraic structure equipped with two binary operations, $\ast$ and $\bigtriangleup$, satisfying specific axioms. This paper investigates a special class of NA-algebras where the operation "$\ast $" exhibits nilpotent properties. We study several fundamental concepts within NA-algebras, including ideals, congruence decomposition, congruence kernels, and multiplicative stabilizers. A notion of NA-morphism is introduced, and a corresponding NA-morphism theorem is established. Furthermore, we explore the relationships between NA-algebras and other related logical algebraic structures, such as quantum B-algebras, Q-algebras, CI-algebras, pseudo-BCH-algebras, and RM-algebras. Notably, we prove that any nilpotent NA-algebra forms a quantum B-algebra. These results lay a foundation for further research into the structure and potential applications of NA-algebras.