Gröbner–Shirshov bases for semirings

In the paper we derive a Gröbner–Shirshov algorithm for semirings and commutative semirings. As applications, we obtain Gröbner–Shirshov bases and A. Blassʼs (1995) and M. Fiore and T. Leinsterʼs (2004) normal forms of the semirings N[x]/(x=1+x+x2) and N[x]/(x=1+x2), correspondingly.

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Bibliographic Details
Published inJournal of algebra Vol. 385; pp. 47 - 63
Main Authors Bokut, L.A., Chen, Yuqun, Mo, Qiuhui
Format Journal Article
LanguageEnglish
Published Elsevier Inc 01.07.2013
Subjects
Congruence
Gröbner–Shirshov basis
Normal form
Semiring
16Y60
Congruence
13P10
Normal form
Gröbner–Shirshov basis
Semiring
16S15
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Summary:In the paper we derive a Gröbner–Shirshov algorithm for semirings and commutative semirings. As applications, we obtain Gröbner–Shirshov bases and A. Blassʼs (1995) and M. Fiore and T. Leinsterʼs (2004) normal forms of the semirings N[x]/(x=1+x+x2) and N[x]/(x=1+x2), correspondingly.
ISSN:0021-8693
1090-266X
DOI:10.1016/j.jalgebra.2013.03.013