EuDML | Browse

In this paper we study restricted Boolean rings and group rings. A ring $R$ is $𝑟𝑒𝑠𝑡𝑟𝑖𝑐𝑡𝑒𝑑𝐵𝑜𝑜𝑙𝑒𝑎𝑛$ if every proper homomorphic image of $R$ is boolean. Our main aim is to characterize restricted Boolean group rings. A complete characterization of non-prime restricted Boolean group rings has been obtained. Also in case of prime group rings necessary conditions have been obtained for a group ring to be restricted Boolean. A counterexample is given to show that these conditions are not sufficient.

Rings consisting entirely of certain elements

Huanyin Chen, Marjan Sheibani, Nahid Ashrafi (2018)

Czechoslovak Mathematical Journal

We completely determine when a ring consists entirely of weak idempotents, units and nilpotents. We prove that such ring is exactly isomorphic to one of the following: a Boolean ring; $ℤ_{3} \oplus ℤ_{3}$ ; $ℤ_{3} \oplus B$ where $B$ is a Boolean ring; local ring with nil Jacobson radical; $M_{2} (ℤ_{2})$ or $M_{2} (ℤ_{3})$ ; or the ring of a Morita context with zero pairings where the underlying rings are $ℤ_{2}$ or $ℤ_{3}$ .

Ring-theoretic properties of Iwasawa algebras: a survey.

Ardakov, K., Brown, K.A. (2007)

Documenta Mathematica

Displaying 1 – 7 of 7

Radicals of semi-group rings

Recent results on the derived length of Lie solvable group algebras.

Remarks on the Lie derived lengths of group algebras of groups with cyclic derived subgroup.

Representations of solvable Lie algebras. II. Twisted group rings

Restricted Boolean group rings

Rings consisting entirely of certain elements

Ring-theoretic properties of Iwasawa algebras: a survey.

Currently displaying 1 – 7 of 7