Gröbner-Shirshov bases for semirings

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.

arXiv comment22 pages

References in corpus (7)

• Groebner-Shirshov bases for dialgebras
• Composition-Diamond Lemma for Tensor Product of Free Algebras
• Groebner-Shirshov Bases: Some New Results
• Gröbner-Shirshov bases for Lie algebras over a commutative algebra
• Gröbner-Shirshov bases for metabelian Lie algebras
• Gröbner-Shirshov bases for some Lie algebras
• Composition-Diamond Lemma for Non-associative Algebras over a Commutative Algebra

Cited by in corpus (3)

• Gröbner-Shirshov bases and their calculation
• Gröbner-Shirshov bases for some Lie algebras
• Gröbner-Shirshov bases and PBW theorems