linearsets

Linearsets are a type of mathematical structure that has gained significant interest in the field of abstract algebra. They are defined as a set of pairs of elements, along with a binary operation that combines each pair in a specific way. In other words, a linearset is a collection of ordered pairs of elements from a set, closed under a binary operation.

The concept of linearsets was first introduced by mathematician Robert Elwell in the 1970s. Since then, they have been studied extensively in various mathematical disciplines, including groups and semigroups. Researchers have explored the properties and applications of linearsets, leading to a deeper understanding of their structure and behavior.

One of the key properties of linearsets is that they can be viewed as a generalization of the concept of a group. While groups have a single binary operation, linearsets have two distinct operations - the binary operation that combines pairs of elements and the operation that results from combining the two operations. This property makes linearsets more flexible and interesting from a mathematical perspective.

Linearsets have potential applications in various areas of mathematics and computer science. They can be used to model real-world systems, such as systems with two types of interactions or hierarchical structures. Further research is needed to fully explore the capabilities and limitations of linearsets. Some of the ongoing research focuses on the study of linearsets with specific algebraic properties, such as idempotence or commutativity.