McAlister covering theorem
A subset in an inverse semigroup is called unitary if for any elements and , or implies .
An inverse semigroup is E-unitary if its semigroup of idempotents is unitary.
Theorem.
Let be an inverse semigroup; then, there exists an E-unitary inverse semigroup and a surjective, idempotent-separating homomorphism .
Also, if is finite, then may be chosen to be finite as well.
Note that a homomorphism is idempotent-separating if it is injective on idempotents.
References
- 1 M. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, World Scientific, 1998
Title | McAlister covering theorem |
---|---|
Canonical name | McAlisterCoveringTheorem |
Date of creation | 2013-03-22 14:37:19 |
Last modified on | 2013-03-22 14:37:19 |
Owner | mathcam (2727) |
Last modified by | mathcam (2727) |
Numerical id | 5 |
Author | mathcam (2727) |
Entry type | Theorem |
Classification | msc 20M18 |
Defines | unitary |
Defines | E-unitary |
Defines | idempotent-separating |