The Binomial Theorem for Algebraic Structures
نویسنده
چکیده
Let L be a non empty loop structure. We say that L is add-left-cancelable if and only if: (Def. 1) For all elements a, b, c of L such that a + b = a + c holds b = c. We say that L is add-right-cancelable if and only if: (Def. 2) For all elements a, b, c of L such that b + a = c + a holds b = c. We say that L is add-cancelable if and only if: (Def. 3) For all elements a, b, c of L holds if a + b = a + c, then b = c and if b + a = c + a, then b = c. One can check the following observations: ∗ there exists a non empty loop structure which is add-left-cancelable,
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