Subrings of zero-dimensional rings

When Sarah Glaz, Bill Heinzer and the junior author of this article approached Robert with the idea of editing a book dedicated to his work, we asked him to give us a list of his work and to comment on it to the extent he felt comfortable. As usual, he was extremely thorough in his response. When the authors of this article began to consider what topic we wanted to write about, we were impressed by Robert’s comment that he was particularly pleased with his series of papers with Bill on the embeddability of a ring in a zero-dimensional ring. So we decided to write about that. Our task was complicated by the fact that Robert had already written several excellent expository papers on the subject [8, 9, 10]. The problem is easy to state.