On the semisimilarity and consemisimilarity of split quaternions (Q297602)

The authors introduce the concept of semisimilarity and consemisimilarity of split quaternions. They also examine the solvability conditions and general solutions of systems of the form \(xay=b\), \(ybx=a\) and \(\tilde{x}ay=b\), \(\tilde{y}bx=a\) in split quaternions. If there exist \(x\) and \(y\) that satisfy the first equations system, then \(a\) and \(b\) are said to be semisimilar. If there exist \(x\) and \(y\) that satisfy the second equations system, then \(a\) and \(b\) are said to be consemisimilar.