In mathematics, absolutely irreducible is a term applied to linear representations or algebraic varieties over a field. It means that the object in question remains irreducible, even after any finite extension of the field of coefficients. In both cases, being absolutely irreducible is the same as being irreducible over the algebraic closure of the ground field.
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Famous quotes containing the words absolutely and/or irreducible:
“He that has his chains knocked off, and the prison doors set open to him, is perfectly at liberty, because he may either go or stay, as he best likes; though his preference be determined to stay, by the darkness of the night, or illness of the weather, or want of other lodging. He ceases not to be free, though the desire of some convenience to be had there absolutely determines his preference, and makes him stay in his prison.”
—John Locke (1632–1704)
“If an irreducible distinction between theatre and cinema does exist, it may be this: Theatre is confined to a logical or continuous use of space. Cinema ... has access to an alogical or discontinuous use of space.”
—Susan Sontag (b. 1933)