Standard bases in mixed power series and polynomial rings over rings
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- 作者：Thomas Markwiga ; keilen@math.uni-tuebingen.de" class="auth_mail" title="E-mail the corresponding author ; Yue Renb ; ren@mathematik.uni-kl.de" class="auth_mail" title="E-mail the corresponding author ; Oliver Wienandb ; wienand@mathematik.uni-kl.de" class="auth_mail" title="E-mail the corresponding author
- 关键词：primary ; 13P10 ; 13F25 ; 16W60 ; secondary ; 12J25 ; 16W60
- 刊名：Journal of Symbolic Computation
- 出版年：2017
- 出版时间：March-April 2017
- 年：2017
- 卷：79
- 期：part_P1
- 页码：119-139
- 全文大小：468 K
文摘
In this paper we study standard bases for submodules of a mixed power series and polynomial ring ormulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116300888&_mathId=si1.gif&_user=111111111&_pii=S0747717116300888&_rdoc=1&_issn=07477171&md5=cee40627550e37aea8491600afdc46a1" title="Click to view the MathML source">R〚t1,…,tm〛[x1,…,xn]s respectively of their localisation with respect to a 75b5697d59849513e5439">
-local monomial ordering for a certain class of noetherian rings R , also called Zacharias rings. The main steps are to prove the existence of a division with remainder generalising and combining the division theorems of Grauert–Hironaka and Mora and to generalise the Buchberger criterion. Everything else then translates naturally. Setting either ormulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116300888&_mathId=si3.gif&_user=111111111&_pii=S0747717116300888&_rdoc=1&_issn=07477171&md5=06916aae867e73c734cee90592cb543b" title="Click to view the MathML source">m=0 or ormulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116300888&_mathId=si4.gif&_user=111111111&_pii=S0747717116300888&_rdoc=1&_issn=07477171&md5=1dd7d530e242c36d0d77082f13993b41" title="Click to view the MathML source">n=0 we get standard bases for polynomial rings respectively for power series rings over R as a special case.
-local monomial ordering for a certain class of noetherian rings R , also called Zacharias rings. The main steps are to prove the existence of a division with remainder generalising and combining the division theorems of Grauert–Hironaka and Mora and to generalise the Buchberger criterion. Everything else then translates naturally. Setting either ormulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116300888&_mathId=si3.gif&_user=111111111&_pii=S0747717116300888&_rdoc=1&_issn=07477171&md5=06916aae867e73c734cee90592cb543b" title="Click to view the MathML source">m=0 or ormulatext stixSupport mathImg" data-mathURL="/science?_ob=MathURL&_method=retrieve&_eid=1-s2.0-S0747717116300888&_mathId=si4.gif&_user=111111111&_pii=S0747717116300888&_rdoc=1&_issn=07477171&md5=1dd7d530e242c36d0d77082f13993b41" title="Click to view the MathML source">n=0 we get standard bases for polynomial rings respectively for power series rings over R as a special case.