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CREATION
Title : Strongly graded rings which are generalized Dedekind rings
Author :

Prof. Dr. Sri Wahyuni, S.U. (1) Hidetoshi Marubayashi (2) Iwan Ernanto S.Si., M.Sc. (3) Dr. Sutopo, S.Si., M.Si. (4)
Date : 31 2020
Keyword : Graded ring; maximal order; Dedekind ring; prime Goldie ring; hereditary Noetherian prime ring. Graded ring; maximal order; Dedekind ring; prime Goldie ring; hereditary Noetherian prime ring.
Abstract : Let $R = \oplus_{n \in \mathbb{Z}} R_n$ be a strongly graded ring of type $\mathbb{Z}$ such that $R_{0}$ is a prime Goldie ring with its quotient ring $Q_{0}$. It is shown that the following three conditions are equivalent: (i) $R_0$ is a $\mathbb{Z}$-invariant generalized Dedekind ring ($G$-Dedekind ring for short), (ii) $R$ is a $G$-Dedekind ring and (iii) $R$ is a graded $G$-Dedekind ring. We describe all invertible ideals of $G$-Dedekind rings in terms of $R_0$ and $Q^g=\oplus_{n\in \mathbb{Z}} Q_{0}R_{n}$. We provide counter-examples of $\mathbb{Z}$-invariant $G$-Dedekind rings which are not $G$-Dedekind rings.
Group of Knowledge : Matematika
Original Language : English
Level : Internasional
Status :
Published
Document
No Title Document Type Action
1 Strongly graded rings which are generalized Dedekind rings.pdf
Document Type : [PAK] Cek Similarity
[PAK] Cek Similarity View
2 Bukti-KORESPONDENSI-STRONGLY-di-Jurnal-JAA.pdf
Document Type : [PAK] Bukti Korespondensi Penulis
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3 Dokumen-Lengkap-Strongly-JAA--.pdf
Document Type : [PAK] Full Dokumen
[PAK] Full Dokumen View
4 WoS-Strongly graded rings which are generalized Dedekind rings-Web of Science Core Collection.pdf
Document Type : Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian)
Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian) View
5 ScimagoJournal of Algebra and its Applications.pdf
Document Type : Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian)
Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian) View
6 Scopus - Document details - Strongly graded rings which are generalized Dedekind rings _ Signed in.pdf
Document Type : Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian)
Dokumen Pendukung Karya Ilmiah (Hibah, Publikasi, Penelitian, Pengabdian) View
7 Strongly graded rings which are generalized Dedekind rings.pdf
Document Type : [PAK] Full Dokumen
[PAK] Full Dokumen View
8 Strongly graded rings which are generalized Dedekind rings.pdf
Document Type : [PAK] Full Dokumen
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9 CS-Strongly graded rings which are generalized Dedekind rings.pdf
Document Type : [PAK] Cek Similarity
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