Torsion-free abelian group 1970-01-01
A **torsion-free abelian group** is an important concept in group theory, a branch of abstract algebra.
Trivial semigroup 1970-01-01
A trivial semigroup is a specific type of algebraic structure in the field of abstract algebra, particularly in the study of semigroups. A semigroup is defined as a set equipped with an associative binary operation. The trivial semigroup is the simplest form of a semigroup, consisting of a single element.
Variety of finite semigroups 1970-01-01
A **variety of finite semigroups** is a class of semigroups that can be defined using certain algebraic properties or operations. More specifically, a variety is generated by a set of finite semigroups and is characterized by the types of identities they satisfy. In algebra, varieties are often used to study structures that share common defining properties, much like varieties in other algebraic contexts (such as groups or rings). ### Key Concepts 1.