Article in volume
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Title:
Quasi-primary ideals in commutative semirings
PDFSource:
Discussiones Mathematicae - General Algebra and Applications 43(1) (2023) 101-110
Received: 2021-05-10 , Revised: 2021-08-29 , Accepted: 2021-10-04 , Available online: 2023-01-11 , https://doi.org/10.7151/dmgaa.1412
Abstract:
In this paper, we define quasi-primary ideals in commutative semirings $S$ with
$1\neq 0$ which is a generalization of primary ideals. A proper ideal $I$ of a
semiring $S$ is said to be a quasi-primary ideal of $S$ if $ab\in \sqrt I$
implies $a\in \sqrt {I}$ or $b\in \sqrt{I}$. We also introduce the concept of
$2$-absoring quasi-primary ideal of a semiring $S$ which is a generalization of
quasi-primary ideal of $S.$ A proper ideal $I$ of a semiring $S$ is said to be
a $2$-absorbing quasi-primary ideal if $abc\in \sqrt I$ implies $ab\in \sqrt {I}$
or $bc\in \sqrt{I}$ or $ac\in \sqrt{I}$. Some basic results related to
$2$-absorbing quasi-primary ideal have also been given.
Keywords:
semiring, subtractive ideal, primary ideal, quasi-primary ideal, $2$-absorbing quasi-primary ideal, $Q$-ideal
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