We use cookies to distinguish you from other users and to provide you with a better experience on our websites. Close this message to accept cookies or find out how to manage your cookie settings.
To save content items to your account,
please confirm that you agree to abide by our usage policies.
If this is the first time you use this feature, you will be asked to authorise Cambridge Core to connect with your account.
Find out more about saving content to .
To save content items to your Kindle, first ensure [email protected]
is added to your Approved Personal Document E-mail List under your Personal Document Settings
on the Manage Your Content and Devices page of your Amazon account. Then enter the ‘name’ part
of your Kindle email address below.
Find out more about saving to your Kindle.
Note you can select to save to either the @free.kindle.com or @kindle.com variations.
‘@free.kindle.com’ emails are free but can only be saved to your device when it is connected to wi-fi.
‘@kindle.com’ emails can be delivered even when you are not connected to wi-fi, but note that service fees apply.
For a field K, let
$\mathcal {R}$
denote the Jacobson algebra
$K\langle X, Y \ | \ XY=1\rangle $
. We give an explicit construction of the injective envelope of each of the (infinitely many) simple left
$\mathcal {R}$
-modules. Consequently, we obtain an explicit description of a minimal injective cogenerator for
$\mathcal {R}$
. Our approach involves realizing
$\mathcal {R}$
up to isomorphism as the Leavitt path K-algebra of an appropriate graph
$\mathcal {T}$
, which thereby allows us to utilize important machinery developed for that class of algebras.
Let R be a left and right perfect right self-injective ring. It is shown that if the radical of R is countably generated as a left ideal then R is quasi-Frobenius. It is also shown that the same conclusion can be drawn if r(A ∩ B) = r(A) + r(B) for all left ideals A and B of R.
Recommend this
Email your librarian or administrator to recommend adding this to your organisation's collection.