The Binomial Theorem for Algebraic Structures1
نویسنده
چکیده
Let us note that every non empty loop structure which is add-left-cancelable and add-rightcancelable is also add-cancelable and every non empty loop structure which is add-cancelable is also add-left-cancelable and add-right-cancelable. Let us note that every non empty loop structure which is Abelian and add-right-cancelable is also add-left-cancelable and every non empty loop structure which is Abelian and add-left-cancelable is also add-right-cancelable. Let us mention that every non empty loop structure which is right zeroed, right complementable, and add-associative is also add-right-cancelable. Let us note that there exists a non empty double loop structure which is Abelian, add-associative, left zeroed, right zeroed, commutative, associative, add-cancelable, distributive, and unital. Next we state two propositions:
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