Year: 2026
Type: article
Abstract: Let R be a commutative ring, and let S=R[Y1,…,Yn] denote the polynomial ring in n variables Y1,…,Yn. We introduce an admissible term order on the monomials in these variables and extend the classical definition of circuits to the case where coefficients lie in a commutative ring R. We investigate the conditions under which an ideal of R[Y1,…,Yn], generated by linear forms, can be generated by R-circuits. Specific results are obtained when R=K[x1,…,xm], which is the polynomial ring over a field K.
Source: Mathematics
DOI: 10.3390/math14081347
Authors: Gioia Failla, Paola Lea Staglianò
Institution: University of Reggio Calabria
Language: English
Subfield: Algebra and Number Theory
Field: Mathematics
Domain: Physical Sciences
Open Access status: gold
Estimated APC paid: $3,137
OpenAlex ID: W7154682403