Details:
Title  Standard basis of a polynomial ideal over commutative Artinian chain ring.  Author(s)  E.V. Gorbatov  Type  Article in Journal  Abstract  e construct a standard basis of an ideal of the polynomial ring R[X] = R[x 1, . . . , x k] over commutative Artinian chain ring R, which generalises a Gröbner base of a polynomial ideal over fields. We adopt the notion of the leading term of a polynomial suggested by D. A. Mikhailov and A. A. Nechaev, but using the simplification schemes introduced by V. N. Latyshev. We prove that any canonical generating system constructed by D. A. Mikhailov and A. A. Nechaev is a standard basis of the special form. We give an algorithm (based on the notion of Spolynomial) which constructs standard bases and canonical generating systems of an ideal. We define minimal and reduced standard bases and give their characterisations. We prove that a Gröbner base χ of a polynomial ideal over the field = R/ rad(R) can be lifted to a standard basis of the same cardinality over R with respect to the natural epimorphism ν : R[X] → [X] if and only if there is an ideal I R[X] such that I is a free Rmodule and Ī = (χ).  ISSN  09249265; 15693929/e 
URL 
http://www.degruyter.com/view/j/dma.2004.14.issue1/156939204774148820/156939204774148820.xml 
Language  English  Journal  Discrete Math. Appl.  Volume  14  Number  1  Pages  5278  Publisher  De Gruyter, Berlin  Year  2004  Edition  0  Translation 
No  Refereed 
No 
