caa a22 4500 378883798 CHVBK 20180305123438.0 cr unu---uuuuu 161128e20040101xx s 000 0 eng 10.1515/156939204774148811 doi (NATIONALLICENCE)gruyter-10.1515/156939204774148811 Solving systems of polynomial equations over Galois-Eisenstein rings with the use of the canonical generating systems of polynomial ideals [Elektronische Daten] [D.A. Mikhailov, A.A. Nechaev] A Galois-Eisenstein ring or a GE-ring is a finite commutative chain ring. We consider two methods of enumeration of all solutions of some system of polynomial equations over a GE-ring R. The first method is the general method of coordinate-wise linearisation. This method reduces to solving the initial polynomial system over the quotient field = R/ Rad R and then to solving a series of linear equations systems over the same field. For an arbitrary ideal of the ring R[x 1, . . . , x k ] a standard base called the canonical generating system (CGS) is constructed. The second method consists of finding a CGS of the ideal generated by the polynomials forming the left-hand side of the initial system of equations and solving instead of the initial system the system with polynomials of the CGS in the left-hand side. For systems of such type a modification of the coordinate-wise linearisation method is presented. Copyright 2004, Walter de Gruyter Mikhailov D.A. aut Nechaev A.A. aut Discrete Mathematics and Applications Walter de Gruyter 14/1(2004-01-01), 41-73 0924-9265 14:1<41 2004 14 dma https://doi.org/10.1515/156939204774148811 text/html Onlinezugriff via DOI 1 research article jats NATIONALLICENCE 856 40 https://doi.org/10.1515/156939204774148811 text/html Onlinezugriff via DOI NATIONALLICENCE 700 1- Mikhailov D.A. aut NATIONALLICENCE 700 1- Nechaev A.A. aut NATIONALLICENCE 773 0- Discrete Mathematics and Applications Walter de Gruyter 14/1(2004-01-01), 41-73 0924-9265 14:1<41 2004 14 dma CC0 http://creativecommons.org/publicdomain/zero/1.0 nationallicence BK010053 XK010053 XK010000 NATIONALLICENCE NATIONALLICENCE NL-gruyter