GOLDIE DIMENSION OF CONSTANTS OF LOCALLY NILPOTENT SKEW DERIVATIONS

2012 ◽  
Vol 11 (06) ◽  
pp. 1250105 ◽  
Author(s):  
JEFFREY BERGEN ◽  
PIOTR GRZESZCZUK
Keyword(s):  
Ore Extension ◽  
Natural Conditions ◽  
Goldie Dimension ◽  
Locally Nilpotent ◽  
Base Ring

In this paper, we examine rings R with locally nilpotent skew derivations d and compare the Goldie dimension of R to that of the subring of constants Rd. This generalizes the situation where one compares the Goldie dimension of an Ore extension to that of the base ring. Under certain natural conditions placed upon Rd, we show that R and Rd have the same Goldie dimension.

Some types of ring elements in Ore extensions over noncommutative rings

2017 ◽  
Vol 16 (11) ◽  
pp. 1750201 ◽  
Author(s):  
E. Hashemi ◽  
M. Hamidizadeh ◽  
A. Alhevaz
Keyword(s):  
Ore Extension ◽  
Von Neumann ◽  
Noncommutative Rings ◽  
Regular Elements ◽  
Derivation Formula ◽  
Von Neumann Regular ◽  
Ore Extensions ◽  
Base Ring ◽  
Extension Ring ◽  
Ring Elements

Let [Formula: see text] be an associative unital ring with an endomorphism [Formula: see text] and [Formula: see text]-derivation [Formula: see text]. Some types of ring elements such as the units and the idempotents play distinguished roles in noncommutative ring theory, and will play a central role in this work. In fact, we are interested to study the unit elements, the idempotent elements, the von Neumann regular elements, the [Formula: see text]-regular elements and also the von Neumann local elements of the Ore extension ring [Formula: see text], when the base ring [Formula: see text] is a right duo ring which is [Formula: see text]-compatible. As an application, we completely characterize the clean elements of the Ore extension ring [Formula: see text], when the base ring [Formula: see text] is a right duo ring which is [Formula: see text]-compatible.

scholarly journals GK DIMENSION AND LOCALLY NILPOTENT SKEW DERIVATIONS

2014 ◽  
Vol 57 (3) ◽  
pp. 555-567
Author(s):  
JEFFREY BERGEN ◽  
PIOTR GRZESZCZUK
Keyword(s):  
Closed Field ◽  
Finitely Generated ◽  
Natural Conditions ◽  
Skew Derivation ◽  
Algebraically Closed Field ◽  
Locally Nilpotent ◽  
Gk Dimension ◽  
Kirillov Dimension

AbstractLet A be a domain over an algebraically closed field with Gelfand–Kirillov dimension in the interval [2,3). We prove that if A has two locally nilpotent skew derivations satisfying some natural conditions, then A must be one of five algebras. All five algebras are Noetherian, finitely generated, and have Gelfand–Kirillov dimension equal to 2. We also obtain some results comparing the Gelfand–Kirillov dimension of an algebra to its subring of invariants under a locally nilpotent skew derivation.

Some open problems on locally finite or locally nilpotent derivations and ℰ-derivations

2018 ◽  
Vol 20 (04) ◽  
pp. 1750056 ◽  
Author(s):  
Wenhua Zhao
Keyword(s):  
Commutative Ring ◽  
Characteristic Zero ◽  
Associative Algebras ◽  
Open Problems ◽  
Integral Domains ◽  
Locally Finite ◽  
Locally Nilpotent ◽  
Base Ring ◽  
Lf Formula ◽  
Algebra Endomorphism

Let [Formula: see text] be a commutative ring and [Formula: see text] an [Formula: see text]-algebra. An [Formula: see text]-[Formula: see text]-derivation of [Formula: see text] is an [Formula: see text]-linear map of the form [Formula: see text] for some [Formula: see text]-algebra endomorphism [Formula: see text] of [Formula: see text], where [Formula: see text] denotes the identity map of [Formula: see text]. In this paper, we discuss some open problems on whether or not the image of a locally finite (LF) [Formula: see text]-derivation or [Formula: see text]-[Formula: see text]-derivation of [Formula: see text] is a Mathieu subspace [W. Zhao, Generalizations of the image conjecture and the Mathieu conjecture, J. Pure Appl. Algebra 214 (2010) 1200–1216; Mathieu subspaces of associative algebras, J. Algebra 350(2) (2012) 245–272] of [Formula: see text], and whether or not a locally nilpotent (LN) [Formula: see text]-derivation or [Formula: see text]-[Formula: see text]-derivation of [Formula: see text] maps every ideal of [Formula: see text] to a Mathieu subspace of [Formula: see text]. We propose and discuss two conjectures which state that both questions above have positive answers if the base ring [Formula: see text] is a field of characteristic zero. We give some examples to show the necessity of the conditions of the two conjectures, and discuss some positive cases known in the literature. We also show some cases of the two conjectures. In particular, both the conjectures are proved for LF or LN algebraic derivations and [Formula: see text]-[Formula: see text]-derivations of integral domains of characteristic zero.

Thierry Kuntzel and the Rise of Video Art

2018 ◽  
Author(s):  
Hilary Radner ◽  
Alistair Fox
Keyword(s):  
New Technology ◽  
Video Art ◽  
Video Technology ◽  
Natural Conditions

Raymond Bellour describes how his interest in video art grew out of his personal friendship with Thierry Kuntzel and the latter’s growing interest in experimental filmmaking using the new technology, and how this interest prompted him to seek to understand how the new medium was leading to a modification of perception. He goes on to explain how video technology enables the production of images that escape the natural conditions deemed to constrain photography, also emphasizing the influence of painting on video art.

GEOGRAPHY OF FREE ECONOMIC ZONES:WORLD EXPERIENCE AND UZBEKISTAN

2020 ◽  
Vol 4 (3) ◽  
pp. 40-51
Author(s):  
Shaxzod Ibragimov ◽  
◽  
Quvonchbek Sag`dullayev ◽  
Bibisora Sadibekova
Keyword(s):  
Geographical Location ◽  
Investment Climate ◽  
Natural Conditions ◽  
Economic Relations ◽  
Investment Projects ◽  
Free Economic Zone ◽  
Economic Zone ◽  
Economic Zones

This article describes geographical foundations of free economic zones. Each free economic zone has a unique economic geographical location, natural conditions and resources. These factors play an important role in the development of free economic zones. Various forms of free economic zones in world countries, territorial investment conditions, their level favorableness and investment climate, maintaining foreign economic relations, as well as the development of investment projects are determined by the geographical indicators of free economic zones

CALCULATION PARAMETERS OF SPRINKLING MACHINES WITH COMBINED FRONTAL AND CIRCULAR MOVEMENT

1970 ◽  
pp. 4-7
Author(s):  
N. N. Dubenok ◽  
G. V. Olgarenko ◽  
B. S. Gordon
Keyword(s):  
Calculated Data ◽  
Irrigation Scheduling ◽  
Natural Conditions ◽  
Linear Mode ◽  
Irrigation Technology ◽  
Irrigated Area ◽  
Center Pivot ◽  
Irrigation Technologies ◽  
The Given ◽  
Operation Characteristics

If the center pivot or linear moving irrigation machines are operated with their own individual irrigation technologies, but the irrigation machines with combined center-pivot and linear moving mode are operated on one field in turn as a center pivot and as a linear. The goal of this work is creation of theoretical base for calculation of improved irrigation machines parameters and existing irrigation equipment modernizing, according to the different natural conditions. The research object is investigation of characteristics of rain delivered from irrigation machines with combined center-pivot and linear moving mode, assuring uniform irrigation distribution according to the irrigation technology and operation parameters, size and configuration of seasonal norm as well as to the irrigation scheduling. The pointed goal is achieved by the given problem solving, when having basic data on the irrigation norm and time, as well as operation characteristics and the irrigation area configuration, the predicted hydro modulus are calculated for the irrigation machine working in a center pivot and in a linear mode. The simulation of sprinkling devices operation on the machine is made by one universal formula, when on the plots irrigated in center pivot and linear mode is achieved equality of arranged hydro modulus to the corresponding calculated data. At that, are considered all the possible combinations of the total irrigated area parts, irrigated with different technologies.

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