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

Finitely-generated Algebra - Examples

... The polynomial

... 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

... 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

... 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

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**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:

“Poetry has become the higher *algebra* of metaphors.”

—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)

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