219 citations · 799 across the 37 of their papers we have counts for
41 papers
Biquasigroups linear over a group
Wieslaw A. Dudek, Robert A. R. Monzo
We determine the structure of biquasigroups (Q,^,*) satisfying varations of Polonijo's Ward double quasigroup identity (x^z)*(y^z)=x*y, including those that are linear over a group…
Pentagonal quasigroups, their translatability and parastrophes
R. A. R. Monzo, W. A. Dudek
Any pentagonal quasigroup is proved to have the product xy = R(x)+y-R(y) where (Q,+) is an Abelian group, R is its regular automorphism satisfying R^4-R^3+R^2-R+1 = 0 and 1 is the…
Double Magma associated with Ward and double Ward quasigroups
W. A. Dudek, R. A. R. Monzo
We describe types of double magma associated with Ward quasigroups, double Ward quasigroups, their duals and the groups they generate. Ward quasigroup double magma and unipotent, r…
The structure of idempotent translatable quasigroups
Wieslaw A. Dudek, Robert A. R. Monzo
We prove the main result that a groupoid of order n is an idempotent k-translatable quasigroup if and only if its multiplication is given by x.y = (ax+by)(mod n), where a+b = 1(mod…
Translatability and translatable semigroups
Wieslaw A. Dudek, Robert A. R. Monzo
The concept of a k-translatable groupoid is explored in depth. Some properties of idempotent k-translatable groupoids, left cancellative k-translatable groupoids and left unitary k…
Parastrophes of quasigroups
Wieslaw A. Dudek
Parastrophes (conjugates) of a quasigroup can be divided into separate classes containing isotopic parastrophes. We prove that the number of such classes is always 1, 2, 3 or 6. Ne…