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 no-reply@cambridge.org
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.
A special atom (respectively, supernilpotent atom) is a minimal element of the lattice $\mathbb{S}$ of all special radicals (respectively, a minimal element of the lattice $\mathbb{K}$ of all supernilpotent radicals). A semiprime ring $R$ is called prime essential if every nonzero prime ideal of $R$ has a nonzero intersection with each nonzero two-sided ideal of $R$. We construct a prime essential ring $R$ such that the smallest supernilpotent radical containing $R$ is not a supernilpotent atom but where the smallest special radical containing $R$ is a special atom. This answers a question put by Puczylowski and Roszkowska.
Recommend this
Email your librarian or administrator to recommend adding this to your organisation's collection.