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Keywords:
$S$-2-absorbing quasi primary ideal; quasi-$S$-primary ideal; $S$-2-absorbing ideal; trivial ring extension; amalgamated algebra
$S$-2-absorbing quasi primary ideal; quasi-$S$-primary ideal; $S$-2-absorbing ideal; trivial ring extension; amalgamated algebra
Summary:
Let $R$ be a commutative ring with identity and $S$ be a multiplicative subset of $R$. We introduce the notion of $S$-2-absorbing quasi primary ideal, which is a generalization of quasi-$S$-primary ideal. We define a proper ideal $I$ of $R$ to be $S$-2-absorbing quasi primary if $\sqrt {I}$ is an $S$-2-absorbing ideal of $R$. Additionally, we define a new class of rings, called $S$-2-$ABQ$ ring. A number of results concerning $S$-2-absorbing quasi primary ideals and $S$-2-$ABQ$ rings are presented. Examples and key results are provided to illustrate these concepts.
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