کد مقاله کد نشریه سال انتشار مقاله انگلیسی نسخه تمام متن
5771928 1630428 2017 42 صفحه PDF دانلود رایگان
عنوان انگلیسی مقاله ISI
Equivariant Hilbert series in non-noetherian polynomial rings
موضوعات مرتبط
مهندسی و علوم پایه ریاضیات اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
Equivariant Hilbert series in non-noetherian polynomial rings
چکیده انگلیسی
We introduce and study equivariant Hilbert series of ideals in polynomial rings in countably many variables that are invariant under a suitable action of a symmetric group or the monoid Inc(N) of strictly increasing functions. Our first main result states that these series are rational functions in two variables. A key is to introduce also suitable submonoids of Inc(N) and to compare invariant filtrations induced by their actions. Extending a result by Hillar and Sullivant, we show that any ideal that is invariant under these submonoids admits a Gröbner basis consisting of finitely many orbits. As our second main result we prove that the Krull dimension and multiplicity of ideals in an invariant filtration grow eventually linearly and exponentially, respectively, and we determine the terms that dominate this growth.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 486, 15 September 2017, Pages 204-245
نویسندگان
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