It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigr...It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.展开更多
A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semi...A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.展开更多
基金Foundation item： Supported by NSF of China（10471112） Supported by Shaanxi Provincial Natural Science Foundation（2005A15） Acknowledgement The authors express their gratitude to the referees for very helpful and detailed comments.
文摘It is well known that there exists the smallest inverse semigroup congruence on an orthodox semigroup. We denote by Y the smallest inverse semigroup congruence on an orthodox semigroup. Let S be a right inverse semigroup. We construct partial orders on S by some kind of its subsemigroups and uncover that partial orders on S have close contact with partial orders on S/Y.
文摘A normal orthodox semigroup is an orthodox semigroup whose idempotent elements form a normal band. We deal with congruences on a normal orthodox semigroup with an inverse transversal. A structure theorem for such semigroup is obtained. Munn(1966) gave a fundamental inverse semigroup. Following Munn's idea, we give a fundamental normal orthodox semigroup with an inverse transversal.
