PlanetMath: McAlister covering theorem

(more info)

Math for the people, by the people.

Main Menu

sections Encyclopædia
Papers
Books
Expositions

meta Requests (192)
Orphanage
Unclass'd (1)
Unproven (490)
Corrections (6)
Classification

talkback Polls
Forums
Feedback
Bug Reports

downloads Snapshots
PM Book

information News
Docs
Wiki
ChangeLog
TODO List
Legalese
About

Entry average rating: No information on entry rating

McAlister covering theorem

(Theorem)

A subset in an inverse semigroup is called unitary if for any elements $x\in X$ and $s\in S$ , $xs\in X$ or $sx\in X$ implies $s\in X$ .

An inverse semigroup is E-unitary if its semigroup of idempotents is unitary.

Theorem 1 Let be an inverse semigroup; then, there exists an E-unitary inverse semigroup and a surjective, idempotent-separating homomorphism $\theta:P\rightarrow S$ .

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.

Bibliography

1: M. Lawson, Inverse Semigroups: The Theory of Partial Symmetries, World Scientific, 1998

"McAlister covering theorem" is owned by mathcam. [ owner history (1) ]

(view preamble)

Also defines:

unitary, E-unitary, idempotent-separating

This object's parent.

Log in to rate this entry.
(view current ratings)

Cross-references: injective, finite, homomorphism, surjective, idempotents, semigroup, implies, inverse semigroup, subset
There are 4 references to this entry.

This is version 2 of McAlister covering theorem, born on 2004-09-21, modified 2004-09-21.
Object id is 6201, canonical name is McAlisterCoveringTheorem.
Accessed 3924 times total.

Classification:

AMS MSC:

20M18 (Group theory and generalizations :: Semigroups :: Inverse semigroups)

Pending Errata and Addenda

None.

Discussion

forum policy

No messages.

Interact