Abstract We introduce differential primary decompositions for ideals in a commutative ring. Ideal membership is characterized by conditions. The minimal number of conditions needed the arithmetic multiplicity. Minimal are unique up to change bases. Our results generalize construction Noetherian operators analytic theory Ehrenpreis–Palamodov, and they offer concise method representing affine sch...

Let Dx, ... , Dr e C[d/dxx, ... , d/dxn) be constant coefficient differential operators with zero constant term. Let S = {fe C[xx,... , x„]\Dj(f) = 0 for all 1 < j < r) be the space of polynomial solutions to the system of simultaneous differential equations Dj(f) = 0. It is proved that S is a module over 3¡(V), the ring of differential operators on the affine scheme V with coordinate ring C[d/...

Given a right ideal I in ring R, the idealizer of R is largest subring which becomes two-sided ideal. In this paper we consider idealizers second Weyl algebra A2, differential operators on k[x,y] (in characteristic 0). Specifically, let f be polynomial x and y defines an irreducible curve whose singularities are all cusps. We show that fA2 A2 always left noetherian, extending work McCaffrey.

In this note, we study the polynomial representation of quantum Olshanetsky-Perelomov system for a finite reflection group $W$ type $B_n$. We endow ring ${\mathbb C} [x_1,\ldots\\\ldots, x_n]$ with structure module over Weyl algebra associated [x_1,\ldots,x_n]^{W}$ invariant polynomials under reflections Then differential operators $W$. use theory namely higher Specht and establish decompositio...

The Capelli identity [1] is one of the best exploited results of the classical invariant theory. It provides a set of distinguished generators C1, . . . ,CN for the centre of the enveloping algebra U(glN ) of the general linear Lie algebra. For any non-negative integer M consider the natural action of the Lie algebra glN in the vector space CN⊗CM . Extend it to the action of the algebra U(glN )...

in this paper, we introduce hybrid of block-pulse functions and bernstein polynomials and derive operational matrices of integration, dual, differentiation, product and delay of these hybrid functions by a general procedure that can be used for other polynomials or orthogonal functions. then, we utilize them to solvedelay differential equations and time-delay system. the method is based upon ex...

A polynomial near-ring can mean one of several things. Here a polynomial near-ring is a near-ring of polynomials with the coefficients from a near-ring in the sense of van der Walt and Bagley. We describe quotients of such polynomial near-rings by principal ideals leading to generalizations of some well-known ring constructions. MSC 2000: 16Y30