%0 Journal Article %A Norton, G.H. %A Salagean, Ana %D 2006 %T Strong Gröbner bases for polynomials over a principal ideal ring %U https://repository.lboro.ac.uk/articles/journal_contribution/Strong_Gr_bner_bases_for_polynomials_over_a_principal_ideal_ring/9401753 %2 https://repository.lboro.ac.uk/ndownloader/files/17018318 %K untagged %K Information and Computing Sciences not elsewhere classified %X Gröbner bases have been generalised to polynomials over a commutative ring A in several ways. Here we focus on strong Gröbner bases, also known as D-bases. Several authors have shown that strong Gröbner bases can be effectively constructed over a principal ideal domain. We show that this extends to any principal ideal ring: we characterise Gröbner bases and strong Gröbner bases when A is a principal ideal ring. We also give algorithms for computing Gröbner bases and strong Gröbner bases which generalise known algorithms to principal ideal rings.In particular, we give an algorithm for computing a strong Gröbner basis over a finite-chain ring, for example a Galois ring. %I Loughborough University