A copy of this work was available on the public web and has been preserved in the Wayback Machine. The capture dates from 2017; you can also visit the original URL.
The file type is
The problem of determining the number of finite central groupoids (an algebraic system satisfying the identity (x . y) . (y -z) = y) is equivalent to the problem of determining the number of solutions of the matrix equation A2 = J, where A is a 0, 1 matrix and J is a matrix of 1's. The existence of solutions of A2 = J of all ranks r, where n < r < [(n2 + 1)/2], and A is n2 x rP, is proven. Since these are the only possible values, the question of existence solutions of all possible ranks isdoi:10.1016/0097-3165(74)90047-8 fatcat:gjwkqmkonfahzm2n7kih3vag6q