4 citations · 20 across the 13 of their papers we have counts for
15 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…
Right, left and double division in semigroups that are semilattices of groups
R. A. R. Monzo
The binary products of right, left or double division in semigroups that are semilattices of groups give interesting groupoid structures that are in one to one correspondence with…
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…