generated set
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Generated collection — In diatonic set theory, a generated collection is a collection or scale formed by repeatedly adding a constant interval in integer notation, the generator, also known as an interval cycle, around the chromatic circle until a complete collection… … Wikipedia
set theory — the branch of mathematics that deals with relations between sets. [1940 45] * * * Branch of mathematics that deals with the properties of sets. It is most valuable as applied to other areas of mathematics, which borrow from and adapt its… … Universalium
Set (music) — Six element set of rhythmic values used in Variazioni canoniche by Luigi Nono[1] A set (pitch set, pitch class set, set class, set form, pitch collection) in music theory, as in mat … Wikipedia
set theory — The modern theory of sets was largely inspired by Cantor, whose proof that the set of real numbers could not be put into a one to one correspondence with the set of natural numbers opened the door to the set theoretic hierarchy, and to the study… … Philosophy dictionary
Finitely generated module — In mathematics, a finitely generated module is a module that has a finite generating set. Equivalently, it is a homomorphic image of a free module on finitely many generators. The kernel of this homomorphism need not be finitely generated (then… … Wikipedia
Generating set of a group — In abstract algebra, a generating set of a group is a subset that is not contained in any proper subgroup of the group. Equivalently, a generating set of a group is a subset such that every element of the group can be expressed as the combination … Wikipedia
Finitely-generated module — In mathematics, a finitely generated module is a module that has a finite generating set. A finitely generated R module also may be called a finite R module or finite over R.[1] Related concepts include finitely cogenerated modules, finitely… … Wikipedia
Boundedly generated group — In mathematics, a group is called boundedly generated if it can be expressed as a finite product of cyclic subgroups. The property of bounded generation is also closely related with the congruence subgroup problem (see harvnb|Lubotzky|Segal|2003) … Wikipedia
Structure theorem for finitely generated modules over a principal ideal domain — In mathematics, in the field of abstract algebra, the structure theorem for finitely generated modules over a principal ideal domain is a generalization of the fundamental theorem of finitely generated abelian groups and roughly states that… … Wikipedia
User-generated content — UGC redirects here. For other uses, see UGC (disambiguation). User generated content (UGC) covers a range of media content available in a range of modern communications technologies. It entered mainstream usage during 2005 having arisen in web… … Wikipedia
Finitely-generated abelian group — In abstract algebra, an abelian group (G,+) is called finitely generated if there exist finitely many elements x1,...,xs in G such that every x in G can be written in the form x = n1x1 + n2x2 + ... + nsxs with integers n1,...,ns. In this case, we … Wikipedia
