Let G be a group and R G-graded ring. In this paper, we present examine the concept of graded weakly 2-absorbing ideals as in generality prime ring which is not commutative, demonstrates that symmetry obtained lot outcomes commutative rings remain are commutative.

In this article, we define a non-commutative deformation of the ”symplectic invariants” (introduced in [13]) of an algebraic hyperelliptical plane curve. The necessary condition for our definition to make sense is a Bethe ansatz. The commutative limit reduces to the symplectic invariants, i.e. algebraic geometry, and thus we define non-commutative deformations of some algebraic geometry quantit...

Duchamp, G. and D. Krob, On the partially commutative shuffle product, Theoretical Computer Science 96 (1992) 405410. We give recursive formulas that allow us to compute the partially commutative shuffle product of two partially commutative words.

The Hamiltonian (gauge) symmetry generators of non-local (gauge) theories are presented. The construction is based on the d + 1 dimensional space-time formulation of d dimensional non-local theories. The procedure is applied to U(1) space-time non-commutative gauge theory. In the Hamiltonian formalism the Hamiltonian and the gauge generator are constructed. The nilpotent BRST charge is also obt...

This paper explores ways of performing commutative tasks by N parties. Tasks are defined as commutative if the order at which parties perform tasks can be freely changed without affecting the final result. It is easy to see that arbitrary N-party commutative tasks cannot be completed in less than N − 1 basic time units. We conjecture that arbitrary N-party commutative tasks cannot be performed ...

This paper deals with some properties of n-fold commutative ideals and n-fold weak commutative ideals in BCK-algebras. Afterwards, we construct some algorithms for studying foldness theory of commutative ideals in BCK-algebras.

‎‎Let $R$ be a non-commutative ring with unity‎. ‎The commuting graph‎ of $R$ denoted by $Gamma(R)$‎, ‎is a graph with a vertex set‎ ‎$Rsetminus Z(R)$ and two vertices $a$ and $b$ are adjacent if and only if‎ $ab=ba$‎. ‎In this paper‎, ‎we investigate non-commutative rings with unity of order $p^n$ where $p$ is prime and $n in lbrace 4,5 rbrace$‎. It is shown that‎, ‎$Gamma(R)$ is the disjoint ...

The Maxwell theory on non-commutative spaces has been considered. The non-linear equations of electromagnetic fields on non-commutative spaces were obtained in the compact spin-tensor (quater-nion) form. We found the symmetric energy-momentum tensor and its non-zero trace. So, the trace anomaly of the energy-momentum tensor was obtained in electrodynamics on non-commutative spaces. It was noted...

A non-commutative polynomial which is positive on a bounded semi-algebraic set of operators has a weighted sum of squares representation. This Positivstellensatz parallels similar results in the commutative case. A broader issue is to what extent does real semi-algebraic geometry extend to non-commutative polynomials? Our ”strict” Positivstellensatz is positive news, on the opposite extreme fro...

We present several results concerning non-commutative instantons and the Seiberg–Witten map. Using a simple ansatz we find a large new class of instanton solutions in arbitrary even dimensional non-commutative Yang–Mills theory. These include the two dimensional “shift operator” solutions and the four dimensional Nekrasov–Schwarz instantons as special cases. We also study how the Seiberg–Witten...