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单词 InversesInRings
释义

inverses in rings


Let R be a ring with unity 1 and rR. Then r is left invertible if there exists qR with qr=1; q is a left inverseMathworldPlanetmath of r. Similarly, r is right invertible if there exists sR with rs=1; s is a right inverse of r.

Note that, if r is left invertible, it may not have a unique left inverse, and similarly for right invertible elements. On the other hand, if r is left invertible and right invertible, then it has exactly one left inverse and one right inverse. Moreover, these two are equal, and r is a unit.

Titleinverses in rings
Canonical nameInversesInRings
Date of creation2013-03-22 17:08:55
Last modified on2013-03-22 17:08:55
OwnerWkbj79 (1863)
Last modified byWkbj79 (1863)
Numerical id4
AuthorWkbj79 (1863)
Entry typeTopic
Classificationmsc 16-00
Related topicKlein4Ring
Related topicLeftAndRightUnityOfRing
Definesleft invertible
Definesright invertible
Definesleft inverse
Definesright inverse
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