Expanding the socle of a codimension 3 complete intersection

Abstract

A quotient ring of a regular local ring of embedding dimension~3 has a minimal free resolution that carries a differential graded algebra structure. This structure has been used to classify such rings. For some classes very few examples have been observed. One such class is called \lt B>{B}\lt /B>, named for Anne Brown, who discovered and gave the first constructions of rings in this class. Her constructions were the only known rings in that class until recently. In this paper, we show how to obtain Artinian rings in the class \textbf {B} by expanding the socle of a complete intersection.