Let R be a commutative ring, and let S=RY1,…,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 RY1,…,Yn, generated by linear forms, can be generated by R-circuits. Specific results are obtained when R=Kx1,…,xm, which is the polynomial ring over a field K.
Failla et al. (Fri,) studied this question.
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