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arXiv · 1805.11928

On 2-absorbing ideals of commutative semirings

Hussein Behzadipour·Peyman Nasehpour
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Abstract

In this paper, we investigate 2-absorbing ideals of commutative semirings and prove that if $\mathfrak{a}$ is a nonzero proper ideal of a subtractive valuation semiring $S$ then $\mathfrak{a}$ is a 2-absorbing ideal of $S$ if and only if $\mathfrak{a}=\mathfrak{p}$ or $\mathfrak{a}=\mathfrak{p}^2$ where $\mathfrak{p}=\sqrt\mathfrak{a}$ is a prime ideal of $S$. We also show that each 2-absorbing ideal of a subtractive semiring $S$ is prime if and only if the prime ideals of $S$ are comparable and if $\mathfrak{p}$ is a minimal prime over a 2-absorbing ideal $\mathfrak{a}$, then $\mathfrak{am} = \mathfrak{p}$, where $\mathfrak{m}$ is the unique maximal ideal of $S$.

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Hussein Behzadipour, Peyman Nasehpour. 2018-05-30. On 2-absorbing ideals of commutative semirings. https://doi.org/10.1142/s0219498820500346

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