commutative ring
algebraic structure
field
commutative ring in which every nonzero element is inversible
excellent ring
a Noetherian universally catenary ring that is J-2 and Grothendieck
center
subring consisting of elements that commute with any element
integral domain
commutative ring with no zero divisors other than zero
catenary ring
commutative ring admitting a good dimension function, i.e. that relative dimension between two prime ideals is well defined, in the sense that any maximal strictly increasing chain of prime ideals between the two has the same finite length
real closed ring
mathematical Rong
adele ring
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"
Boolean ring
mathematical concept
arithmetical ring
commutative ring whose lattice of ideals is distributive
representation ring
the Grothendieck ring of the monoidal category of (e.g. finite-dimensional complex) representations of a (e.g. compact Lie) group
normal ring
commutative ring whose localizations at prime ideals are integrally closed domains
Boolean algebra
lattice that models the classical propositional logic
abelian von Neumann algebra
von Neumann algebra in which all elements commute