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Loose edges and factorization theorems
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-23 , DOI: 10.1090/proc/14720 Janusz Gwoździewicz , Beata Hejmej , Bernd Schober
Proceedings of the American Mathematical Society ( IF 0.8 ) Pub Date : 2021-03-23 , DOI: 10.1090/proc/14720 Janusz Gwoździewicz , Beata Hejmej , Bernd Schober
Abstract:Let 
be a regular local ring with maximal ideal 
. We consider elements 
such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of 
to such an edge is a product of two coprime polynomials, then 
factorizes in the 
-adic completion.
中文翻译：
边缘松散和因式分解定理
摘要：让具有最大理想的规则局部环成为可能。我们考虑这样的元素，使它们的牛顿多面体具有宽松的边缘。我们证明，如果对这样的边缘的符号限制是两个互质多项式的乘积，则将-adic补全分解。
更新日期：2021-04-22
be a regular local ring with maximal ideal . We consider elements such that their Newton polyhedron has a loose edge. We show that if the symbolic restriction of to such an edge is a product of two coprime polynomials, then factorizes in the -adic completion. 中文翻译：
边缘松散和因式分解定理
摘要：让
具有最大理想的规则局部环成为可能。我们考虑这样的元素，使它们的牛顿多面体具有宽松的边缘。我们证明，如果对这样的边缘的符号限制是两个互质多项式的乘积，则将-adic补全分解。 
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