Bol loop (original) (raw)
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, or a strengthened form of (left or right) alternativity.
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| dbo:abstract | 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, or a strengthened form of (left or right) alternativity. A loop is both left Bol and right Bol if and only if it is a Moufang loop. Alternatively, a right or left Bol loop is Moufang if and only if it satisfies the flexible identity a(ba) = (ab)a . Different authors use the term "Bol loop" to refer to either a left Bol or a right Bol loop. (en) |
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| rdfs:comment | 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, or a strengthened form of (left or right) alternativity. (en) |
| rdfs:label | Bol loop (en) |
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