Abstract
Let R be commutative ring with . A proper ideal I of R is called a 1-absorbing primary ideal of R if whenever nonunit elements
and
, then
or
. It is proved that every primary ideal of R is 1-absorbing primary and every 1-absorbing primary ideal of R is semi-primary (that is ideals with prime radical). However, these three concepts are different. In this paper, we characterize rings R over which every semi-primary ideal is 1-absorbing primary and (resp. Noetherian) rings R over which every 1-absorbing primary ideal is prime (resp. primary). Many examples are given to illustrate the obtained results.
Correction Statement
This article has been republished with minor changes. These changes do not impact the academic content of the article.
Acknowledgments
The authors would like to thank the referee for careful reading of the manuscript.