Commutative Ring Theory, Commutative Rings and Symmetry

A special issue of Symmetry (ISSN 2073-8994). This special issue belongs to the section "Mathematics".

Deadline for manuscript submissions: closed (31 March 2021) | Viewed by 2717

Special Issue Editor

Bar Ilan University
Interests: algebra; ring theory; Specht problem; combinatorial geometry; affine algebraic geometry
Special Issues, Collections and Topics in MDPI journals

Special Issue Information

Dear Colleagues,

Quantum mechanics methods provide solutions of some classical problems of noncommutative algebra and algebraic geometry. For example, an equivalence between famous Jacobian and Dixmier conjectures [1,2] was established via an anti-quantization procedure, with infinitely large primes playing the role of a plank constant. The Kontsevich conjecture about canonical isomorphism between symmetry groups: ploynomial symplectoauthomorphisms and authomorphsisms of Weil algebra depicts the equivariance of quantization procedure [3].

This view point provides relation between quantization and symmetry is certainly one of many, the variety of which can provide some fruitful discussion.

Prof. Alexei Kanel-Belov
Guest Editor

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Keywords

  • quantization
  • Weil algebra, Kontsevich quantization theorem
  • polynomial authomorphisms and quantization
  • dequantization
  • Poisson brackets, symmetry, equivariant quantization

Published Papers (1 paper)

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Research

48 pages, 454 KiB  
Article
New Types of Permuting n-Derivations with Their Applications on Associative Rings
by Mehsin Jabel Atteya
Symmetry 2020, 12(1), 46; https://0-doi-org.brum.beds.ac.uk/10.3390/sym12010046 - 25 Dec 2019
Viewed by 1913
Abstract
In this article, we introduce new generators of a permuting n-derivations to improve and increase the action of usual derivation. We produce a permuting n-generalized semiderivation, a permuting n-semigeneralized semiderivation, a permuting n-antisemigeneralized semiderivation and a permuting skew n [...] Read more.
In this article, we introduce new generators of a permuting n-derivations to improve and increase the action of usual derivation. We produce a permuting n-generalized semiderivation, a permuting n-semigeneralized semiderivation, a permuting n-antisemigeneralized semiderivation and a permuting skew n-antisemigeneralized semiderivation of non-empty rings with their applications. Actually, we study the behaviour of those types and present their results of semiprime ring R. Examples of various results have also been included. That is, many of the branches of science such as business, engineering and quantum physics, which used a derivation, have the opportunity to invest them in solving their problems. Full article
(This article belongs to the Special Issue Commutative Ring Theory, Commutative Rings and Symmetry)
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