Quasi-duo differential polynomial rings

Differential Polynomial Rings of Triangular Matrix Rings

Quasi-Duo Rings and Stable Range Descent

In a recent paper, the first author introduced a general theory of corner rings in noncommutative rings that generalized the classical theory of Peirce decompositions. This theory is applied here to the study of the stable range of rings upon descent to corner rings. A ring is called quasi-duo if every maximal 1-sided ideal is 2-sided. Various new characterizations are obtained for such rings. ...

differential polynomial rings of triangular matrix rings

Modules over Differential Polynomial Rings

This note announces a number of results on the structure of differential modules over differential rings, where differential ring means a ring with a family of derivations and differential module means a module having a family of operators compatible with the derivations of the ring. To fix notation, throughout the paper we let A denote an associative ring, M = AM an 4-module, k the correspondi...

On the Differential Simplicity of Polynomial Rings

Commutative differentially simple rings have proved to be quite useful as a source of examples in non-commutative algebra. In this paper we use the theory of holomorphic foliations to construct new families of derivations with respect to which the polynomial ring over a field of characteristic zero is differentially simple.