variety of algebras

A variety of algebras is a broad category in mathematics that groups together all algebraic systems sharing common rules or properties, like groups, rings, or fields. Think of it as a family or class of mathematical structures defined by specific axioms or operations. For example, all groups follow rules about how elements combine and invert, forming a variety. These classifications help mathematicians study and understand different algebraic systems by focusing on their shared properties and exploring how they differ when certain rules are added, removed, or modified.