Karya
Judul/Title Strongly graded rings which are generalized Dedekind rings
Penulis/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)
Tanggal/Date 31 2020
Kata Kunci/Keyword
Abstrak/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.
Rumpun Ilmu Matematika
Bahasa Asli/Original Language English
Level Internasional
Status
Dokumen Karya
No Judul Tipe Dokumen Aksi
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