On the structure of braces satisfying the maximal condition on ideals

In this article we delve into the study of braces satisfying the maximal condition on ideals. We call them i-noetherian braces. The main goal of this article is to show a brace-theoretical analogue of a well-known result of Hall for metabelian groups: we prove that a 2-multipermutational brace is i-noetherian if, and only if, it is finitely generated as a brace. An example of an i-noetherian brace that does not satisfy the maximal condition on subbraces follows naturally from our main result.