The prime spectrum of algebras of quadratic growth

We study prime algebras of quadratic growth. Our first result is that if $A$ is a prime monomial algebra of quadratic growth then $A$ has finitely many prime ideals $P$ such that $A/P$ has GK dimension one. This shows that prime monomial algebras of quadratic growth have bounded matrix images. We next show that a prime graded algebra of quadratic growth has the property that the intersection of the nonzero prime ideals $P$ such that $A/P$ has GK dimension 2 is non-empty, provided there is at least one such ideal. From this we conclude that a prime monomial algebra of quadratic growth is either primitive or has nonzero locally nilpotent Jacobson radical. Finally, we show that there exists a prime monomial algebra $A$ of GK dimension two with unbounded matrix images and thus the quadratic growth hypothesis is necessary to conclude that there are only finitely many prime ideals such that $A/P$ has GK dimension 1.Comment: 23 page

Stop And Search Pilot Evaluation Report

In the context of increased attention and scrutiny regarding stop and search in Scotland, the introduction of Police Scotland’s stop and search pilot, which aims to improve data recording practices,accountability and community confidence in the use of stop and search, is to be welcomed. Prior to this surprisingly little research or academic attention had been devoted to stop and search in Scotland, save some notable exceptions (see Background, Section 2 below). Police Scotland selected ‘P’ Division as thepilot site and the pilot was launched in Fife in July 2014, with support being provided by the National Stop and Search Unit. An independent academic evaluation was commissioned at the end of that month, with an expectation that the final report would be delivered in March 2015. Our tender was accepted inAugust 2014 and we began our work in September 2014, with our researcher arriving in mid-November 2014. We concluded our data collection period in February 2015...

Stop And Search Pilot Evaluation Report

In the context of increased attention and scrutiny regarding stop and search in Scotland, the introduction of Police Scotland’s stop and search pilot, which aims to improve data recording practices,accountability and community confidence in the use of stop and search, is to be welcomed. Prior to this surprisingly little research or academic attention had been devoted to stop and search in Scotland, save some notable exceptions (see Background, Section 2 below). Police Scotland selected ‘P’ Division as thepilot site and the pilot was launched in Fife in July 2014, with support being provided by the National Stop and Search Unit. An independent academic evaluation was commissioned at the end of that month, with an expectation that the final report would be delivered in March 2015. Our tender was accepted inAugust 2014 and we began our work in September 2014, with our researcher arriving in mid-November 2014. We concluded our data collection period in February 2015...

Golod-Shafarevich algebras, free subalgebras and Noetherian images

It is shown that Golod-Shaferevich algebras of a reduced number of defining relations contain noncommutative free subalgebras in two generators, and that these algebras can be homomorphically mapped onto prime, Noetherian algebras with linear growth. It is also shown that Golod-Shafarevich algebras of a reduced number of relations cannot be nil

SPRINGS WITH CALCAREOUS TUFA IN THE VALLEY OF THE JAMNE CREEK IN GORCE

The study gives a detail characteristic of a hard water springs habitat with the communities of Cratoneurion commutati (habitat code of Nature 2000: 7220), localized within Nature 2000 protected area Ostoja Gorczańska PLH120018, in an upper part of the valley of Jamne creek. The plants are described along with the main habitat parameters, namely: altitude, exposition, slope gradient, insolation, type of bedrock, water flow regime and the spring outflow efficiency. The temperature, pH, electrical conductivity were measured in the field, the concentrations of Ca and Mg in spring water were measured by Atomic Absorption Spectroscopy (AAS). The investigated headwater areas are small (0.7–80 m2) and highly differentiated by the intensity of calcareous tufa precipitation and the degree of plant cover development

On a conjecture of Goodearl: Jacobson radical non-nil algebras of Gelfand-Kirillov dimension 2

For an arbitrary countable field, we construct an associative algebra that is graded, generated by finitely many degree-1 elements, is Jacobson radical, is not nil, is prime, is not PI, and has Gelfand-Kirillov dimension two. This refutes a conjecture attributed to Goodearl

Towards Our Common Digital Future. Flagship Report.

In the report “Towards Our Common Digital Future”, the WBGU makes it clear that sustainability strategies and concepts need to be fundamentally further developed in the age of digitalization. Only if digital change and the Transformation towards Sustainability are synchronized can we succeed in advancing climate and Earth-system protection and in making social progress in human development. Without formative political action, digital change will further accelerate resource and energy consumption, and exacerbate damage to the environment and the climate. It is therefore an urgent political task to create the conditions needed to place digitalization at the service of sustainable development