This article examines annihilators in the skew polynomial ring $R[x;alpha,delta]$. A ring is strongly right $AB$ if everynon-zero right annihilator is bounded. In this paper, we introduce and investigate a particular class of McCoy rings which satisfy Property ($A$) and the conditions asked by P.P. Nielsen. We assume that $R$ is an ($alpha$,$delta$)-compatible ring, and prove that, if $R$ is ni...

The structure of half-BPS representations psu$(2,2|4)$ leads to the definition a super-polynomial ring $\mathcal{R}(8|8)$ which admits realisation in terms differential operators on super-ring. character fundamental field representation encodes resolution an exact sequence modules $\mathcal{R}(8|8)$. is realized by quotienting super-ring quadratic ideal, equivalently setting zero certain polyno...

We introduce a special type of reduction in the ring of differential polynomials and develop the appropriate technique of characteristic sets that allows to generalize the classical Kolchin’s theorem on differential dimension polynomial and find new differential birational invariants of a finitely generated differential field extension. 2000 Mathematics Subject Classification. 12H05, 12H20, 13N15.

In this paper, some properties of $alpha$-skew Armendariz and central Armendariz rings have been studied by variety of others. We generalize the notions to central $alpha$-skew Armendariz rings and investigate their properties. Also, we show that if $alpha(e)=e$ for each idempotent $e^{2}=e in R$ and $R$ is $alpha$-skew Armendariz, then $R$ is abelian. Moreover, if $R$ is central $alpha$-skew A...

‎this paper obtains the exact solutions of the wave equation as a second-order partial differential equation (pde)‎. ‎we are going to calculate polynomial and non-polynomial exact solutions by using lie point symmetry‎. ‎we demonstrate the generation of such polynomial through the medium of the group theoretical properties of the equation‎. ‎a generalized procedure for polynomial solution is pr...

We characterize the principal differential ideals of a polynomial ring in n indeterminates with coefficients in the ring of differential polynomials in n indeterminates and derivation given by a “general” element of Lie(GLn) and use this characterization to construct a generic Picard-Vessiot extension for GLn. In the case when the differential base field has finite transcendence degree over its...

We consider differential rings of the form (k[x,y],D), where k is an algebraically closed field characteristic zero and D:k[x,y]→k[x,y] a k-derivation. study Automorphism Group such ring give criteria for deciding whether that group algebraic group. In most cases, from we deduce primary classification this type up to conjugation with polynomial automorphism.

An ideal in a polynomial ring encodes system of linear partial differential equations with constant coefficients. Primary decomposition organizes the solutions to PDE. This paper develops novel structure theory for primary ideals ring. We characterize terms PDE, punctual Hilbert schemes, relative Weyl algebras, and join construction. Solving PDE described by amounts computing Noetherian operato...

Gröbner bases over polynomial rings have been used for many years in computational algebra, and the other chapters in this book bear witness to this fact. In the mid-eighties some important steps were made in the theory of Gröbner bases in non-commutative rings, notably in rings of differential operators. This chapter is about some of the applications of this theory to problems in commutative a...