Abstract
We introduce and investigate the concept of flexibility in a groupoid, and extend it to RM-algebras, and present several examples and these properties. We observe that condition flexibility is strong, and most known algebras of logic will be trivial with this condition. It is proved that every KL-algebra and BE-algebra are flexible, and every flexible CI-algebra is a BE- algebra. We present that the flexible groups are trivial. Moreover, we apply two conditions (I) and (H) in a groupoid and prove that in a RM-algebra, they will be equivalent.
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