Finite generation refers to the property of a mathematical structure where a set of elements can generate the entire structure through finite combinations. In the context of algebraic structures such as groups, modules, or abelian varieties, finite generation indicates that there exists a finite set of generators from which all elements can be derived. This concept is essential in understanding the nature of solutions to equations over elliptic curves and has significant implications for their structure and behavior.
congrats on reading the definition of Finite Generation. now let's actually learn it.