Abstract
An ideal I of a commutative ring R is called a weakly primary ideal of R if whenever a, b is an element of R and 0 not equal ab is an element of I, then a is an element of I or b is an element of root I. An ideal I of R is called weakly 1-absorbing primary if whenever nonunit elements a, b, c is an element of R and 0 not equal abc is an element of I, then ab is an element of I or c is an element of root L In this paper, we characterize rings over which every ideal is weakly 1-absorbing primary (resp. weakly primary). We also prove that, over a non-local reduced ring, every weakly 1-absorbing primary ideals is weakly primary.