[3][4][1] In 2002, Patrick Jordan introduced the term boset as an abbreviation of biordered set.
According to Mohan S. Putcha, "The axioms defining a biordered set are quite complicated.
David Easdown simplified the definition and formulated the axioms in a special arrow notation invented by him.
The partial binary operation ⋆ on E defined by makes E a biordered set.
Let the symbol (abc) denote the map for which 1 → a, 2 → b, and 3 → c. The set E of idempotents in S contains the following elements: The following table (taking composition of mappings in the diagram order) describes the partial binary operation in E. An X in a cell indicates that the corresponding multiplication is not defined.