Projection invariant extending rings

摘要

A ring R is said to be right pi-extending if every projection invariant right ideal of R is essential in a direct summand of R. In this article, we investigate the transfer of the pi-extending condition between a ring R and its various ring extensions. More specifically, we characterize the right pi-extending generalized triangular matrix rings; and we show that if R-R is pi-extending, then so is T-T where T is an overring of R which is an essential extension of R, an n x n upper triangular matrix ring of R, a column finite or column and row finite matrix ring over R, or a certain type of trivial extension of R.