The varieties of loops of Bol-Moufang type
نویسندگان
چکیده
منابع مشابه
The Varieties of Loops of Bol-Moufang Type
A loop identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, and the order in which the variables appear on both sides is the same, viz. ((xy)x)z = x(y(xz)). Loop varieties defined by one identity of Bol-Moufang type include groups, Bol loops, Moufang loops and C-loops. We show that there are exactly 14 such varietie...
متن کاملThe Varieties of Quasigroups of Bol-moufang Type: an Equational Reasoning Approach
A quasigroup identity is of Bol-Moufang type if two of its three variables occur once on each side, the third variable occurs twice on each side, the order in which the variables appear on both sides is the same, and the only binary operation used is the multiplication, viz. ((xy)x)z = x(y(xz)). Many well-known varieties of quasigroups are of Bol-Moufang type. We show that there are exactly 26 ...
متن کاملOn the Universality of Some Smarandache Loops of Bol-moufang Type
A Smarandache quasigroup(loop) is shown to be universal if all its f, g-principal isotopes are Smarandache f, g-principal isotopes. Also, weak Smarandache loops of Bol-Moufang type such as Smarandache: left(right) Bol, Moufang and extra loops are shown to be universal if all their f, g-principal isotopes are Smarandache f, gprincipal isotopes. Conversely, it is shown that if these weak Smaranda...
متن کاملLoops of Bol-Moufang type with a subgroup of index two
We describe all constructions for loops of Bol-Moufang type analogous to the Chein construction M(G, ∗, g0) for Moufang loops. Mathematics subject classification: 20N05.
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ژورنال
عنوان ژورنال: Algebra universalis
سال: 2005
ISSN: 0002-5240,1420-8911
DOI: 10.1007/s00012-005-1941-1