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- W2038713091 abstract "In this paper, we define the free<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$A$><mml:mi>A</mml:mi></mml:math>-ring over<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$K$><mml:mi>K</mml:mi></mml:math>on a set<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$X$><mml:mi>X</mml:mi></mml:math>, categorically, and parallel some results from the theory of free algebras. We show that the free<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$A$><mml:mi>A</mml:mi></mml:math>-ring over<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$K$><mml:mi>K</mml:mi></mml:math>on<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$X$><mml:mi>X</mml:mi></mml:math>, denoted by<mml:math xmlns:mml=http://www.w3.org/1998/Math/MathML alttext=$A_K left{ X right}$><mml:msub><mml:mi>A</mml:mi><mml:mi>K</mml:mi></mml:msub><mml:mrow><mml:mo>{</mml:mo><mml:mi>X</mml:mi><mml:mo>}</mml:mo></mml:mrow></mml:math>, is graded." @default.
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- W2038713091 date "1993-01-01" @default.
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- W2038713091 title "The freeA-ring is a gradedA-ring" @default.
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- W2038713091 doi "https://doi.org/10.1155/s0161171293000766" @default.
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