کد مقاله | کد نشریه | سال انتشار | مقاله انگلیسی | نسخه تمام متن |
---|---|---|---|---|
5772830 | 1413388 | 2017 | 11 صفحه PDF | دانلود رایگان |
عنوان انگلیسی مقاله ISI
On the class group and S-class group of formal power series rings
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موضوعات مرتبط
مهندسی و علوم پایه
ریاضیات
اعداد جبر و تئوری
پیش نمایش صفحه اول مقاله
چکیده انگلیسی
Let Clt(A) denote the t-class group of an integral domain A. P. Samuel has established that if A is a Krull domain then the mapping Clt(A)âClt(AãXã), is injective and if A is a regular UFD, then Clt(A)âClt(AãXã), is bijective. Later, L. Claborn extended this result in case A is a regular Noetherian domain. In the first part of this paper we prove that the mapping Clt(A)âClt(AãXã); [I]â¦[(I.AãXã)t] is an injective homomorphism and in case of an integral domain A such that each Ï
-invertible Ï
-ideal of A has Ï
-finite type, we give an equivalent condition for Clt(A)âClt(AãXã), to be bijective, thus generalizing the result of Claborn. In the second part of this paper, we define the S-class group of an integral domain A: let S be a (not necessarily saturated) multiplicative subset of an integral domain A. Following [11], a nonzero fractional ideal I of A is S-principal if there exist an sâS and aâI such that sIâaAâI. The S-class group of A, S-Clt(A) is the group of fractional t-invertible t-ideals of A under t-multiplication modulo its subgroup of S-principal t-invertible t-ideals of A. We generalize some known results developed for the classic contexts of Krull and PÏ
MD domain and we investigate the case of isomorphism S-Clt(A)âS-Clt(AãXã).
ناشر
Database: Elsevier - ScienceDirect (ساینس دایرکت)
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 11, November 2017, Pages 2869-2879
Journal: Journal of Pure and Applied Algebra - Volume 221, Issue 11, November 2017, Pages 2869-2879
نویسندگان
Hamed Ahmed, Hizem Sana,