algebraic closure in a sentence
1) The overline denotes the operation of algebraic closure .
algebraic collocations
2) In general, all algebraic closures of a field are isomorphic.
3) Uniqueness of algebraic closure (for a countable field).
algebraic closure example sentences
4) The field of complex numbers is the algebraic closure of the field of real numbers.5) There are several ways to represent the solution in an algebraic closure , which are discussed below.
6) The existence of an algebraic closure for a countable field (but not its uniqueness).
7) In these cases, one refers to such a as "an" algebraic closure of "F".
8) It is the algebraic closure of all the fields in the system, and is denoted by: __FORMULA__.
9) For example, if "F" = Q, the algebraic closure is also called "field of algebraic numbers".
10) It uses the fact that, for a zero-dimensional system, the solutions belong to the algebraic closure of the field "k" of the coefficients of the system.
11) The integral closure Z"p"cl of the "p"-adic integers is also a local ring, with field of fractions Q"p"cl (the algebraic closure of "p"-adic numbers).
12) Finitary closure operators that generalize these two operators are studied in model theory as dcl (for "definable closure") and acl (for " algebraic closure ").
13) If "F" is any field, the separable closure "F"sep of "F" is the field of all elements in an algebraic closure of "F" that are separable over "F".
14) By contrast, the algebraic closure of __FORMULA__, denoted __FORMULA__, has infinite degree, i.e. __FORMULA__ has infinitely many inequivalent algebraic extensions.
15) Even if we do not construct our fields this way, we can still speak of the algebraic closure , but some more delicacy is required in its construction.
example sentences with algebraic closure
16) Suppose given a field "E", and a field "G" containing "E" as a subfield, for example "G" could be the algebraic closure of "E".17) Compared to , the algebraic closure of Q, which also contains all algebraic numbers, C has the advantage of being easily understandable in geometric terms.
18) For example, C is the algebraic closure of R.
19) Together with the above-mentioned fact that C is algebraically closed, this also shows that C is an algebraic closure of R.
20) which maps "K" to the (finite) set of embeddings of "K" into an algebraic closure of "k".
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