In this work we introduce the concept of weak idempotent element as a generalization of the concept of idempotent element and to investigate  weak idempotents in and in some type of group rings. It is shown that if n is  square free integer, then every element of is weak idempotent. Characterization of a weak idempotent in where G is a cyclic group of order 2 is given. Also it is proved that an element of where G is a cyclic group of order is weak idempotent if and only if it has an odd number of summands.

Published 01 August 2018

DOI: 10.14500/icpas2018.pma94

http://dx.doi.org/10.14500/icpas2018.pma94