Topological algebra

ring where ring operations are continuous

commutative ring, whose elements (called adeles) are an infinite tuple of elements from each completion of a number field, such that a cofinite number of them lie in the ring of algebraic integers; "adele" is short for "additive ideal element"

in algebra, any of several related functors on rings and modules that result in complete topological rings and modules

algebraic structure that is complete relative to a metric