Projection invariant extending rings

Abstract

A ring R is said to be right ?-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 ?-extending condition between a ring R and its various ring extensions. More specifically, we characterize the right ?-extending generalized triangular matrix rings; and we show that if RR is ?-extending, then so is TT where T is an overring of R which is an essential extension of R, an n × 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. © 2016 World Scientific Publishing Company.