تقرير
Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebras
العنوان: | Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebras |
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المؤلفون: | Lännström, Daniel |
سنة النشر: | 2018 |
المجموعة: | Mathematics |
مصطلحات موضوعية: | Mathematics - Rings and Algebras, 16P20, 16P40, 16W50, 16S35 |
الوصف: | Let $G$ be a group with neutral element $e$ and let $S=\bigoplus_{g \in G}S_g$ be a $G$-graded ring. A necessary condition for $S$ to be noetherian is that the principal component $S_e$ is noetherian. The following partial converse is well-known: If $S$ is strongly-graded and $G$ is a polycyclic-by-finite group, then $S_e$ being noetherian implies that $S$ is noetherian. We will generalize the noetherianity result to the recently introduced class of epsilon-strongly graded rings. We will also provide results on the artinianity of epsilon-strongly graded rings. As our main application we obtain characterizations of noetherian and artinian Leavitt path algebras with coefficients in a general unital ring. This extends a recent characterization by Steinberg for Leavitt path algebras with coefficients in a commutative unital ring and previous characterizations by Abrams, Aranda Pino and Siles Molina for Leavitt path algebras with coefficients in a field. Secondly, we obtain characterizations of noetherian and artinian unital partial crossed products. |
نوع الوثيقة: | Working Paper |
URL الوصول: | http://arxiv.org/abs/1808.10163 |
رقم الأكسشن: | edsarx.1808.10163 |
قاعدة البيانات: | arXiv |
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