algebra of sets
a nonempty collection of sets having the property that the union of two sets of the collection is a set of the collection and the complement of each set of the collection is a set in the collection. Cf. Boolean ring.

* * *

Universalium. 2010.

### Look at other dictionaries:

• Algebra of sets — The algebra of sets develops and describes the basic properties and laws of sets, the set theoretic operations of union, intersection, and complementation and the relations of set equality and set inclusion. It also provides systematic procedures …   Wikipedia

• algebra of sets — Math. a nonempty collection of sets having the property that the union of two sets of the collection is a set of the collection and the complement of each set of the collection is a set in the collection. Cf. Boolean ring …   Useful english dictionary

• Simple theorems in the algebra of sets — Elementary discrete mathematics courses sometimes leave students under an erroneous impression that the subject matter of set theory is the algebra of union, intersection, and complementation of sets. Those topics are treated below: they would… …   Wikipedia

• Field of sets — Set algebra redirects here. For the basic properties and laws of sets, see Algebra of sets. In mathematics a field of sets is a pair where X is a set and is an algebra over X i.e., a non empty subset of the power set of X closed under the… …   Wikipedia

• Ring of sets — In mathematics, a nonempty collection of sets mathcal{R} is called a ring (of sets) if it is closed under intersection and symmetric difference. That is, for any A,Binmathcal{R}, #A cap B in mathcal{R} #A riangle B in mathcal{R}where riangle… …   Wikipedia

• Algebra — This article is about the branch of mathematics. For other uses, see Algebra (disambiguation). Algebra is the branch of mathematics concerning the study of the rules of operations and relations, and the constructions and concepts arising from… …   Wikipedia

• algebra, modern — ▪ mathematics Introduction also called  abstract algebra        branch of mathematics concerned with the general algebraic structure of various sets (such as real numbers (real number), complex numbers (complex number), matrices (matrix), and… …   Universalium

• algebra — /al jeuh breuh/, n. 1. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such relations. 2. any of… …   Universalium

• Algebra over a field — This article is about a particular kind of vector space. For other uses of the term algebra , see algebra (disambiguation). In mathematics, an algebra over a field is a vector space equipped with a bilinear vector product. That is to say, it is… …   Wikipedia

• algebra — al•ge•bra [[t]ˈæl dʒə brə[/t]] n. 1) math. the branch of mathematics that deals with general statements of relations, utilizing letters and other symbols to represent specific sets of numbers, values, vectors, etc., in the description of such… …   From formal English to slang