کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8904748 | 1633756 | 2018 | 34 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Verbally prime T-ideals and graded division algebras
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
ریاضیات (عمومی)
پیش نمایش صفحه اول مقاله
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چکیده انگلیسی
Let F be an algebraically closed field of characteristic zero and let G be a finite group. We consider graded Verbally prime T-ideals in the free G-graded algebra. It turns out that equivalent definitions in the ordinary case (i.e. ungraded) extend to nonequivalent definitions in the graded case, namely verbally prime G-graded T-ideals and strongly verbally prime T-ideals. At first, following Kemer's ideas, we classify G-graded verbally prime T-ideals. The main bulk of the paper is devoted to the stronger notion. We classify G-graded strongly verbally prime T-ideals which are T-ideal of affine G-graded algebras or equivalently G-graded T-ideals that contain a Capelli polynomial. It turns out that these are precisely the T-ideal of G-graded identities of finite dimensional G-graded, central over F (i.e. Z(A)e=F) which admit a G-graded division algebra twisted form over a field k which contains F or equivalently over a field k which contains enough roots of unity (e.g. a primitive n-root of unity where n=ord(G)).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Advances in Mathematics - Volume 332, 9 July 2018, Pages 142-175
Journal: Advances in Mathematics - Volume 332, 9 July 2018, Pages 142-175
نویسندگان
Eli Aljadeff, Yaakov Karasik,