Group-Derived and Non-Group-Derived Dual $BG$-Algebra
DOI:
https://doi.org/10.29020/nybg.ejpam.v18i4.6974Keywords:
$BG$-algebra, dual $BG$-algebra, dual algebra, group-derived algebraAbstract
This study introduces the notion of the dual BG-algebra. The axioms are presented and are shown to be independent. Fundamental properties of the dual BG-algebra are also provided. The concept of a group-derived dual BG-algebra and its characterization were established. Moreover, a non-group-derived dual BG-algebra can be constructed from a set containing at least 3 elements. Lastly, this paper also presented a Python script used to verify whether a given Cayley table is a dual BG-algebra. This was utilized throughout the process of this study.
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Copyright (c) 2025 Clive Martin G. Chan, Katrina B. Fuentes
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