Finitely Generated Algebra

Some articles on algebra, finitely generated, generated, finitely generated algebra, algebras, finitely:

Finitely-generated Algebra - Examples
... The polynomial algebra K is finitely generated ... The polynomial algebra in countably many generators is infinitely generated ... The field E = K(t) of rational functions in one variable over a given field K is not a finitely generated algebra over K ...
Integral Element - Integral Closure - Finiteness of Integral Closure
... extension, then the integral closure of A in L is a finitely generated A-module ... Let A be a finitely generated algebra over a field k that is an integral domain with field of fractions K ... If L is a finite extension of K, then the integral closure of A in L is a finitely generated A-module and is also a finitely generated k-algebra ...
Separable Algebra - Separable Extensions For Noncommutative Rings
... Notice that an R-R-bimodule (see module theory and homological algebra) restricts to an S-S-bimodule ... separable extensions are many including first separable algebras where R = separable algebra and S = 1 times the ground field ... separable extension over the subring S generated by 1 and bRa ...
Small Cancellation Theory - Applications
... Finitely presented C'(1/6) small cancellation groups are basic examples of word-hyperbolic groups ... Finitely presented groups given by finite C(4)–T(4) presentations where every piece has length one are basic examples of CAT(0) groups for such a ... countable group can be embedded into a simple group generated by an element of order two and an element of order three ...

Famous quotes containing the words algebra and/or generated:

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    José Ortega Y Gasset (1883–1955)

    It is precisely the purpose of the public opinion generated by the press to make the public incapable of judging, to insinuate into it the attitude of someone irresponsible, uninformed.
    Walter Benjamin (1892–1940)