کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772746 | 1413383 | 2017 | 15 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Finitistic dimension conjecture and radical-power extensions
ترجمه فارسی عنوان
بعد فکری و اندیشه های قدرت رادیکال
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
The finitistic dimension conjecture asserts that any finite-dimensional algebra over a field has finite finitistic dimension. Recently, this conjecture is reduced to studying finitistic dimensions for extensions of algebras. In this paper, we investigate those extensions of Artin algebras in which some radical-power of smaller algebras is a nonzero one-sided ideal of bigger algebras. Our result can be formulated for an arbitrary ideal as follows: Let BâA be an extension of Artin algebras and I an ideal of B such that the full subcategory of B/I-modules is B-syzygy-finite. (1) If the extension is right-bounded (for example, Gpd(AB)<â), IArad(B)âB and findim(A)<â, then findim(B)<â. (2) If Irad(B) is a left ideal of A and A is torsionless-finite, then findim(B)<â. Particularly, if I is specified to a power of the radical of B, then our result not only generalizes some of results in the literature (see Corollary 1.2), but also provides new ways to detect algebras of finite finitistic dimensions.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 4, April 2017, Pages 832-846
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 4, April 2017, Pages 832-846
نویسندگان
Chengxi Wang, Changchang Xi,