On Two Conjectures of Abel Grassmann’s Groupoids
AbstractThe quasi-cancellativity of Abel Grassmann‘s groupoids (AG-groupoids) are discussed and two conjectures are partially solved. First, the following conjecture is proved to be true: every AG-3-band is quasi-cancellative. Moreover, a new notion of AG-(4,1)-band is proposed, and it is also proved that every AG-(4,1)-band is quasi-cancellative. Second, the notions of left (right) quasi-cancellative AG-groupoids and power-cancellative AG-groupoids are proposed, and the following results are obtained: for an AG*-groupoid or AG**-groupoid, it is left quasi-cancellative if and only if it is right quasi-cancellative; for a power-cancellative and locally power-associative AG-groupoid, it is left quasi-cancellative if and only if it is right quasi-cancellative. Finally, a general result is proved, that for any AG-groupoid, if it is left quasi-cancellative then it is right quasi-cancellative. View Full-Text
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Zhang, X.; Ma, Y.; Yu, P. On Two Conjectures of Abel Grassmann’s Groupoids. Symmetry 2019, 11, 816.
Zhang X, Ma Y, Yu P. On Two Conjectures of Abel Grassmann’s Groupoids. Symmetry. 2019; 11(6):816.Chicago/Turabian Style
Zhang, Xiaohong; Ma, Yingcang; Yu, Peng. 2019. "On Two Conjectures of Abel Grassmann’s Groupoids." Symmetry 11, no. 6: 816.
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