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#### Open Access in DiVA

####

#### Authority records

Lännström, Daniel
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Lännström, Daniel
##### By organisation

Department of Mathematics and Natural Sciences
On the subject

Algebra and Logic
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The structure of epsilon-strongly group graded ringsPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true});
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2021 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

##### Place, publisher, year, edition, pages

Karlskrona: Blekinge Tekniska Högskola, 2021.
##### Series

Blekinge Institute of Technology Doctoral Dissertation Series, ISSN 1653-2090 ; 3
##### Keywords [en]

group graded ring, Leavitt path algebra, partial crossedproduct, Cuntz-Pimsner ring, von Neumann regular ring, non-unital ring
##### National Category

Algebra and Logic
##### Research subject

Mathematics and applications
##### Identifiers

URN: urn:nbn:se:bth-21342ISBN: 978-91-7295-421-2 (print)OAI: oai:DiVA.org:bth-21342DiVA, id: diva2:1546251
##### Public defence

2021-09-01, Zoom/J1630, 15:00 (English)
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PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt506",{id:"formSmash:j_idt506",widgetVar:"widget_formSmash_j_idt506",multiple:true}); Available from: 2021-04-21 Created: 2021-04-21 Last updated: 2021-06-14Bibliographically approved
##### List of papers

The development of a general theory of strongly group graded rings was initiated by Dade, Năstăsescu and Van Oystaeyen in the 1980s, and since then numerous structural results have been established. In this thesis we develop a general theory of so-called (nearly) epsilon-strongly group graded rings which were recently introduced by Nystedt, Öinert and Pinedo and which generalize strongly group graded rings. Moreover, we obtain applications to Leavitt path algebras, unital partial crossed products and algebraic Cuntz-Pimsner rings.

This thesis is based on five scientific papers (A, B, C, D, E).

Papers A and B are concerned with structural properties of epsilon-strongly graded rings. In Paper A, we consider an important construction called the induced quotient group grading. In Paper B, using results from Paper A, we obtain a Hilbert Basis Theorem for epsilon-strongly graded rings. In Paper C, we study the graded structure of algebraic Cuntz-Pimsner rings. In particular, we obtain a partial characterization of unital strongly graded, epsilon-strongly graded and nearly epsilon-strongly graded algebraic Cuntz-Pimsner rings up to graded isomorphism.

In Paper D, we give a complete characterization of group graded rings that are graded von Neumann regular.

Finally, in Paper E, written in collaboration with Lundström, Öinert and Wagner, we consider prime nearly epsilon-strongly graded rings. Generalizing Passman's work from the 1980s, we give necessary and sufficient conditions for a nearly epsilon-strongly graded ring to be prime.

1. Chain conditions for epsilon-strongly graded rings with applications to Leavitt path algebras$(function(){PrimeFaces.cw("OverlayPanel","overlay1304134",{id:"formSmash:j_idt563:0:j_idt567",widgetVar:"overlay1304134",target:"formSmash:j_idt563:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. A characterization of graded von Neumann regular rings with applications to Leavitt path algebras$(function(){PrimeFaces.cw("OverlayPanel","overlay1474662",{id:"formSmash:j_idt563:1:j_idt567",widgetVar:"overlay1474662",target:"formSmash:j_idt563:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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5. Prime group graded rings with applications to partial crossed products and Leavitt path algebras$(function(){PrimeFaces.cw("OverlayPanel","overlay1556102",{id:"formSmash:j_idt563:4:j_idt567",widgetVar:"overlay1556102",target:"formSmash:j_idt563:4:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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