  Let R be a commutative ring with $1\neq0$. In this paper, we introduce the
concept of weakly 1-absorbing primary ideal which is a generalization of
1-absorbing ideal. A proper ideal $I$ of $R$ is called a weakly 1-absorbing
primary ideal if whenever nonunit elements $a,b,c\in R$ and $0\neq abc\in I,$
then $ab\in I$ or $c\in\sqrt{I}$. A number of results concerning weakly
1-absorbing primary ideals and examples of weakly 1-absorbing primary ideals
are given. Furthermore, we give the correct version of a result on 1-absorbing
ideals of commutative rings.

Rings and Algebras