Nambooripad order information

In mathematics, Nambooripad order^[1] (also called Nambooripad's partial order) is a certain natural partial order on a regular semigroup discovered by K S S Nambooripad^[2] in late seventies. Since the same partial order was also independently discovered by Robert E Hartwig,^[3] some authors refer to it as Hartwig–Nambooripad order.^[4] "Natural" here means that the order is defined in terms of the operation on the semigroup.

In general Nambooripad's order in a regular semigroup is not compatible with multiplication. It is compatible with multiplication only if the semigroup is pseudo-inverse (locally inverse).

^ Thomas Scott Blyth (2005). Lattices and ordered algebraic structures. Springer. pp. 228–232. ISBN 978-1-85233-905-0.
^ K.S.S. Nambooripad (1980). "The natural partial order on a regular semigroup". Proceedings of the Edinburgh Mathematical Society. 23 (3): 249–260. doi:10.1017/s0013091500003801.
^ R. Hartwig (1980). "How to partially order regular elements". Mathematica Japonica. 25 (1): 1–13.
^ J.B. Hickey (2004). "On regularity preservation on a semigroup". Bulletin of the Australian Mathematical Society. 69: 69–86. doi:10.1017/s0004972700034274.

[1] Thomas Scott Blyth (2005). Lattices and ordered algebraic structures. Springer. pp. 228–232. ISBN 978-1-85233-905-0.

[2] K.S.S. Nambooripad (1980). "The natural partial order on a regular semigroup". Proceedings of the Edinburgh Mathematical Society. 23 (3): 249–260. doi:10.1017/s0013091500003801.

[3] R. Hartwig (1980). "How to partially order regular elements". Mathematica Japonica. 25 (1): 1–13.

[4] J.B. Hickey (2004). "On regularity preservation on a semigroup". Bulletin of the Australian Mathematical Society. 69: 69–86. doi:10.1017/s0004972700034274.

Nambooripad order information

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Nambooripad order

Inverse semigroup

Regular semigroup

Epigroup

Biordered set