Commutative von Neumann regular rings are 1-Gröbner | Zendy

Zoran Z. Petrović | Zendy; Maja Roslavcev | Zendy

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Commutative von Neumann regular rings are 1-Gröbner

Author(s) -

Zoran Z. Petrović,

Maja Roslavcev

Publication year - 2021

Publication title -

applicable analysis and discrete mathematics

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.69

H-Index - 26

eISSN - 2406-100X

pISSN - 1452-8630

DOI - 10.2298/aadm210419030p

Subject(s) - mathematics , von neumann regular ring , von neumann architecture , commutative ring , ring (chemistry) , pure mathematics , polynomial ring , principal ideal ring , commutative property , ideal (ethics) , property (philosophy) , gröbner basis , von neumann algebra , noncommutative ring , abelian von neumann algebra , primitive ring , basis (linear algebra) , algebra over a field , mathematical analysis , jordan algebra , polynomial , geometry , algebra representation , law , philosophy , chemistry , epistemology , organic chemistry , political science

Let R be a commutative von Neumann regular ring. We show that every finitely generated ideal I in the ring of polynomials R[X] has a strong Gr?bner basis. We prove this result using only the defining property of a von Neumann regular ring.

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