One-generated semirings and additive divisibility

Korbelář, Miroslav; Landsmann, Günter

doi:10.1142/s0219498817500384

Search citation statements

Order By: Relevance

Paper Sections

Select...

Theorem 11 ([1] Proposition 12)1

Citation Types

Supporting

Mentioning

Contrasting

Year Published

2017

2024

Publication Types

Select...

Article5

Relationship

Self Cite0

Independent5

Authors

Journals

Cited by 5 publications

(1 citation statement)

References 11 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…This result then provides new tools for attacking the conjecture in the case of more generators [11]. Some partial results have also been obtained for a generalization of this problem to divisible semirings (instead of semifields) [12], [13], [14].…”

Section: Theorem 11 ([1] Proposition 12)mentioning

confidence: 99%

Semifields and a theorem of Abhyankar

Kala¹

2017

Commentationes Mathematicae Universitatis Carolinae

View full text Add to dashboard Cite

Abstract. Abhyankar [1] proved that every field of finite transcendence degree over Q or over a finite field is a homomorphic image of a subring of the ring of polynomials Z[T 1 , . . . , Tn] (for some n depending on the field). We conjecture that his result can not be substantially strengthened and show that our conjecture implies a well-known conjecture on the additive idempotence of semifields that are finitely generated as semirings [2], [7].

show abstract

Section: Theorem 11 ([1] Proposition 12)mentioning

confidence: 99%