کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
8895766 | 1630402 | 2018 | 27 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
Descent and ascent of perinormality in some ring extension settings
ترجمه فارسی عنوان
فرود و صعود ناهنجاری در برخی از تنظیمات
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کلمات کلیدی
موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
چکیده انگلیسی
In this paper, we investigate some open questions regarding perinormal domains posed by Neal Epstein and Jay Shapiro in [6]. More specifically, we focus on the ascent/descent property of perinormality between “canonical” integral domain extensions, in particular, AâA[X] and AâAË. We give special conditions under which perinormality ascends from A to the polynomial ring A[X] in the case of an universally catenary domain A. Whereas we have a characterizing result for when perinormality descends from A[X] to A, the sufficient condition for the descent is cumbersome to check. For this reason, we turn to special cases for which perinormality descends from A[X] to A. In the case of an analytically irreducible local domain (A,m) and its m-adic completion (AË,mË), we refer to a technique for generating examples in which perinormality fails to ascend. When AË is perinormal, we explore hypotheses under which A must be normal, perinormal, or weakly normal. Finally, we make connexions between the concepts of semi-normality, weak-normality, relative and global perinormality, and normality.
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Algebra - Volume 512, 15 October 2018, Pages 189-215
Journal: Journal of Algebra - Volume 512, 15 October 2018, Pages 189-215
نویسندگان
Andrew McCrady, Dana Weston,