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Let $R$ be a commutative ring with identity. We study the concept of strongly 1-absorbing primary ideals which is a generalization of $n$-ideals and a subclass of $1$-absorbing primary ideals. A proper ideal $I$ of $R$ is called strongly 1-absorbing primary if for all nonunit elements $a,b,c\in R$ such that $abc\in I$, it is either $ab\in I$ or $c\in \sqrt{0}$. Some properties of strongly 1-absorbing primary ideals are studied. Finally, rings $R$ over which every semi-primary ideal is strongly 1-absorbing primary, and rings $R$ over which every strongly...