Cleanness of overrings of polynomial rings

Differential Polynomial Rings of Triangular Matrix Rings

Polynomial overrings of Int(Z)

We show that every polynomial overring of the ring Int(Z) of polynomials which are integer-valued over Z may be considered as the ring of polynomials which are integer-valued over some subset of Ẑ, the profinite completion of Z with respect to the fundamental system of neighbourhoods of 0 consisting of all non-zero ideals of Z.

Strong cleanness of matrix rings over commutative rings

Let R be a commutative local ring. It is proved that R is Henselian if and only if each R-algebra which is a direct limit of module finite R-algebras is strongly clean. So, the matrix ring Mn(R) is strongly clean for each integer n > 0 if R is Henselian and we show that the converse holds if either the residue class field of R is algebraically closed or R is an integrally closed domain or R is ...

differential polynomial rings of triangular matrix rings

OVERRINGS OF PRIMITIVE FACTOR RINGS OF U(sl(2,C))

This paper shows that certain primitive factor rings of U(sl(2,C)) embed in the rings of differential operators 9 on the curves yz =x “+I There is an action of SL(2,C) as automorphisms . of a making %i a (sl(2) x s1(2),SL(2)) Harish-Chandra bimodule in such a way that the invariant subring under the centre of SL(2), @, i s the primitive factor of U(sl(2)). This result describes all the Dixmier ...