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In mathematics and abstract algebra, a Bol loop is an algebraic structure generalizing the notion of group. Bol loops are named for the Dutch mathematician Gerrit Bol who introduced them in . A loop, ''L'', is said to be a left Bol loop if it satisfies the identity :, for every ''a'',''b'',''c'' in ''L'', while ''L'' is said to be a right Bol loop if it satisfies :, for every ''a'',''b'',''c'' in ''L''. These identities can be seen as weakened forms of associativity. A loop is both left Bol and right Bol if and only if it is a Moufang loop. Different authors use the term "Bol loop" to refer to either a left Bol or a right Bol loop. ==Bruck loops== A Bol loop satisfying the ''automorphic inverse property,'' (''ab'')−1 = ''a''−1 ''b''−1 for all ''a,b'' in ''L'', is known as a (left or right) Bruck loop or K-loop (named for the American mathematician Richard Bruck). The example in the following section is a Bruck loop. Bruck loops have applications in special relativity; see Ungar (2002). Left Bruck loops are equivalent to Ungar's (2002) gyrocommutative gyrogroups, even though the two structures are defined differently. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「Bol loop」の詳細全文を読む スポンサード リンク
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