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arXiv · 1208.0538

Gröbner-Shirshov bases for semirings

L. A. Bokut·Yuqun Chen·Qiuhui Mo
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Abstract

In the paper, we establish Gröbner-Shirshov bases for semirings and commutative semirings. As applications, we obtain Gröbner-Shirshov bases and A. Blass's (1995) and M. Fiore -T. Leinster's (2004) normal forms of the semirings $\mathbb{N}[x]/(x=1+x+x^2)$ and $\mathbb{N}[x]/(x=1+x^2)$ with one generator $x$ and one defining relation, correspondingly.

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L. A. Bokut, Yuqun Chen, Qiuhui Mo. 2012-07-20. Gröbner-Shirshov bases for semirings. https://doi.org/10.1016/j.jalgebra.2013.03.013

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