Ideal Theory in Rings (Translation of "Idealtheorie in Ringbereichen" by Emmy Noether)

This paper is a translation of the paper "Idealtheorie in Ringbereichen", written by Emmy Noether in 1920, from the original German into English. It in particular brings the language used into the modern world so that it is easily understandable by the mathematicians of today. The paper itself deals with ideal theory, and was revolutionary in its field, that is modern algebra. Topics covered include: the representation of an ideal as the least common multiple of irreducible ideals; the representation of an ideal as the least common multiple of maximal primary ideals; the association of prime ideals with primary ideals; the representation of an ideal as the least common multiple of relatively prime irreducible ideals; isolated ideals; the representation of an ideal as the product of coprime irreducible ideals; equivalent concepts regarding modules.Comment: 51 pages, including a page dedicated to notes on the translation of particular term

Graph of groups decompositions of graph braid groups

We provide an explicit construction that allows one to easily decompose a graph braid group as a graph of groups. This allows us to compute the braid groups of a wide range of graphs, as well as providing two general criteria for a graph braid group to split as a non-trivial free product, answering two questions of Genevois. We also use this to distinguish certain right-angled Artin groups and graph braid groups. Additionally, we provide an explicit example of a graph braid group that is relatively hyperbolic, but is not hyperbolic relative to braid groups of proper subgraphs. This answers another question of Genevois in the negative.Comment: Version accepted for publication. Several minor corrections and clarifications have been made and new classes of examples have been added. Code is also available, implementing algorithms in this paper to compute free splittings and presentations of graph braid groups; see https://github.com/danberlyne/graph-braid-splitter and https://github.com/danberlyne/graph-braid-presente

Hierarchical hyperbolicity of graph products

We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this result to answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on any graph product forms a hierarchically hyperbolic space, and that graph products of hierarchically hyperbolic groups are themselves hierarchically hyperbolic groups. This last result is a strengthening of a result of Berlai and Robbio by removing the need for extra hypotheses on the vertex groups. We also answer two questions of Genevois about the geometry of the electrification of a graph product of finite groups.Comment: 63 pages, 12 figures. Comments welcom

Hierarchical Hyperbolicity of Graph Products and Graph Braid Groups

This thesis comprises three original contributions by the author concerning hierarchical hyperbolicity, a coarse geometric tool developed by Behrstock, Hagen, and Sisto to provide a common framework for studying aspects of non-positive curvature in a wide variety of groups and spaces. We show that any graph product of finitely generated groups is hierarchically hyperbolic relative to its vertex groups. We apply this to answer two questions of Genevois about the electrification of a graph product of finite groups. We also answer two questions of Behrstock, Hagen, and Sisto: we show that the syllable metric on a graph product forms a hierarchically hyperbolic space, and that graph products of hierarchically hyperbolic groups are themselves hierarchically hyperbolic groups. This last result is a strengthening of a result of Berlai and Robbio by removing the need for extra hypotheses on the vertex groups. To achieve this, we develop a technique that allows an almost hierarchically hyperbolic structure to be promoted to a hierarchically hyperbolic structure. This technique has found independent use in work of Abbott, Behrstock, and Durham, where it is used to significantly streamline their proofs. We then turn to graph braid groups, using their structure as fundamental groups of special cube complexes to endow them with a natural hierarchically hyperbolic structure. By expressing this structure in terms of the graph, we obtain characterisations of when these groups are hyperbolic or acylindrically hyperbolic. We also conjecture and partially prove a similar characterisation of relative hyperbolicity

The role of photograph aesthetics on online review sites:Effects of management- versus traveler-generated photos on tourists’ decision-making

Tourists searching for information about destinations on online review sites areconcurrently exposed to two different photograph aesthetics, professional (produced by destination managers) and amateur (generated by travelers). While the former is glossy and sharp, the latter is often grainy and overexposed. Although aesthetics are important factors in tourist decision-making, the effects of the exposure to both types of photo aesthetics remain largely unexamined. This research investigates how both types of aesthetics, either singularly or in combination, affect a destination’s visual appeal and tourists’ booking intentionsthrough four controlled experiments (N = 1282). Our results show that despite the ‘messy’ beauty in amateur aesthetics, photos with professional aesthetics make a depicted destinationappear more visually appealing, ultimately driving booking intentions. However, the negative effects of amateur aesthetics are mitigated when (i) viewed by risk-averse tourists, (ii) presented alongside positive reviews, and (iii) accompanied by a greater number of professional photos

The Prevalence and Influence of the Combination of Humor and Violence in Super Bowl Commercials

The growing concern over violence in the media has led to vast amounts of research examining the effects of violent media on viewers. An important subset of this research looks at how humor affects this relationship. While research has considered this subset in television programming, almost no research has explored this in the context of advertising. This paper builds on the little research that exists by examining the effects of combining humor and violence, as well as the theoretical approaches that underlie these effects. A content analysis is conducted to identify the prevalence of violence, humor, and the combination of these elements in a longitudinal sample of Super Bowl commercials (2005, 2007, and 2009). Further, we investigate the relationship between the joint occurrence of humor and violence in ads and ad popularity. We conclude that violent acts are rampant in these commercials and that many acts are camouflaged by the simultaneous presence of humor, especially in the most popular ads

Psychologie spéculative et scientifique de l'esthétique

Berlyne Daniel Ellis. Psychologie spéculative et scientifique de l'esthétique. In: Bulletin de psychologie, tome 30 n°329, 1977. Nouvelles perspectives en psychologie de l'art. pp. 618-621