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finitely generated field

См. также в других словарях:

  • Finitely generated algebra — In mathematics, a finitely generated algebra is an associative algebra A over a field K such that every element of A can be expressed as a polynomial in a finite set of elements a 1, hellip;, a n of A , with coefficients in K . If it is necessary …   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

  • 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

  • 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

  • Field arithmetic — In mathematics, field arithmetic is a subject that studies the interrelations between arithmetic properties of a ql|field (mathematics)|field and its absolute Galois group.It is an interdisciplinary subject as it uses tools from algebraic number… …   Wikipedia

  • Global field — In mathematics, the term global field refers to either of the following:*a number field, i.e., a finite extension of Q or *the function field of an algebraic curve over a finite field, i.e., a finitely generated field of characteristic p >0 of… …   Wikipedia

  • Field (mathematics) — This article is about fields in algebra. For fields in geometry, see Vector field. For other uses, see Field (disambiguation). In abstract algebra, a field is a commutative ring whose nonzero elements form a group under multiplication. As such it …   Wikipedia

  • Algebraic number field — In mathematics, an algebraic number field (or simply number field) F is a finite (and hence algebraic) field extension of the field of rational numbers Q. Thus F is a field that contains Q and has finite dimension when considered as a vector… …   Wikipedia

  • Function field of an algebraic variety — In algebraic geometry, the function field of an algebraic variety V consists of objects which are interpreted as rational functions on V . In complex algebraic geometry these are meromorphic functions and their higher dimensional analogues; in… …   Wikipedia

  • Adjunction (field theory) — In abstract algebra, adjunction is a construction in field theory, where for a given field extension E / F , subextensions between E and F are constructed. Definition Let E be a field extension of a field F . Given a set of elements A in the… …   Wikipedia

  • Pseudo algebraically closed field — In mathematics, a field K is pseudo algebraically closed (usually abbreviated by PAC) if one of the following equivalent conditions holds:*Each absolutely irreducible variety V defined over K has a K rational point. *Each absolutely irreducible… …   Wikipedia

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