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Forum Mathematicum

Managing Editor: Bruinier, Jan Hendrik

Ed. by Blomer, Valentin / Cohen, Frederick R. / Droste, Manfred / Duzaar, Frank / Echterhoff, Siegfried / Frahm, Jan / Gordina, Maria / Shahidi, Freydoon / Sogge, Christopher D. / Takayama, Shigeharu / Wienhard, Anna


IMPACT FACTOR 2018: 0.867

CiteScore 2018: 0.71

SCImago Journal Rank (SJR) 2018: 0.898
Source Normalized Impact per Paper (SNIP) 2018: 0.964

Mathematical Citation Quotient (MCQ) 2018: 0.71

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1435-5337
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Volume 28, Issue 5

Issues

Annelidan rings

Greg Marks
  • Corresponding author
  • Department of Mathematics and Computer Science, St. Louis University, St. Louis, MO 63103, United States of America
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/ Ryszard Mazurek
Published Online: 2015-11-17 | DOI: https://doi.org/10.1515/forum-2015-0107

Abstract

We introduce the class of right annelidan rings, defined by the property that any annihilator right ideal of the ring is comparable with every right ideal of the ring. This class is a common generalization of the classes of domains and right uniserial rings. We obtain results on the structure of right annelidan rings; in particular, we show that all right annelidan rings are Armendariz. We study the relationships between right annelidan rings, chain conditions, and 2-primal rings. For the class of right annelidan rings, we prove a version of the Hopkins–Levitzki Theorem for principal right ideals. We characterize right annelidan group algebras, obtaining a classification that is complete if the zero-divisor problem has a positive solution.

Keywords: Annelidan ring; lineal ring

MSC 2010: 16D25; 16L30; 16N40; 16P60; 16S34; 16D20; 16P40; 16S70; 16U80

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About the article


Received: 2015-06-04

Revised: 2015-10-08

Published Online: 2015-11-17

Published in Print: 2016-09-01


The first author received support from a Summer Research Award from St. Louis University’s Office of Research Services. The second author was supported by Polish KBN Grant 1 P03A 032 27.


Citation Information: Forum Mathematicum, Volume 28, Issue 5, Pages 923–941, ISSN (Online) 1435-5337, ISSN (Print) 0933-7741, DOI: https://doi.org/10.1515/forum-2015-0107.

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