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In mathematics, especially abstract algebra, loop theory and quasigroup theory are active research areas with many open problems.As in other areas of mathematics, such problems are often made public at professional conferences and meetings.
One can normalize a Cayley table of a quasigroup in the same manner as a reduced Latin square. Then the quasigroup associated to a reduced Latin square has a (two sided) identity element (namely, the first element among the row headers). A quasigroup with a two sided identity is called a loop. Some, but not all, loops are groups.
The integers Z (or the rationals Q or the reals R) with subtraction (−) form a quasigroup. These quasigroups are not loops because there is no identity element (0 is a right identity because a − 0 = a, but not a left identity because, in general, 0 − a ≠ a). The nonzero rationals Q × (or the nonzero reals R ×) with division (÷) form ...
Download as PDF; Printable version; ... This category is intended for all unsolved problems in mathematics, ... List of problems in loop theory and quasigroup theory;
Download as PDF; Printable version; ... List of problems in loop theory and quasigroup theory; ... Polarization of an algebraic form;
In mathematics, the theory of Latin squares is an active research area with many open problems. As in other areas of mathematics, such problems are often made public at professional conferences and meetings. Problems posed here appeared in, for instance, the Loops (Prague) conferences and the Milehigh (Denver) conferences.
This cheat sheet is the aftermath of hours upon hours of research on all of the teams in this year’s tournament field. I’ve listed each teams’ win and loss record, their against the spread totals, and
Talk: List of problems in loop theory and quasigroup theory. Add languages. Page contents not supported in other languages. ... Download as PDF; Printable version