Let R be a commutative ring, and let S=R[Y1,& mldr;,Yn] denote the polynomial ring in n variables Y1,& mldr;,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,& mldr;,Yn], generated by linear forms, can be generated by R-circuits. Specific results are obtained when R=K[x1,& mldr;,xm], which is the polynomial ring over a field K.
On Ideals Generated by R-Circuits / Failla, G., Stagliano, P.L.. - In: MATHEMATICS. - ISSN 2227-7390. - 14:8(2026), pp. 1-16. [10.3390/math14081347]
On Ideals Generated by R-Circuits
Failla G.
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2026-01-01
Abstract
Let R be a commutative ring, and let S=R[Y1,& mldr;,Yn] denote the polynomial ring in n variables Y1,& mldr;,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,& mldr;,Yn], generated by linear forms, can be generated by R-circuits. Specific results are obtained when R=K[x1,& mldr;,xm], which is the polynomial ring over a field K.I documenti in IRIS sono protetti da copyright e tutti i diritti sono riservati, salvo diversa indicazione.
