Open AccessCommutative von Neumann regular rings are 1-Gröbner
Author(s) -
Z Petrović,
Maja Roslavcev
Publication year - 2022
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.