Purity, Algebraic Compactness, Direct Sum Decompositions, and Representation Type

By B. Huisgen‐Zimmermann. 2014

64 citations recorded by the source corpus.

The idea of purity pervades human culture, from religion through sexual and moral codes, cleansing rituals and dietary rules, to stratifications of societies into castes. It does so to an extent which is hardly backed up by the following definition found in the Oxford English Dictionary: freedom from admixture of any foreign substance or matter. In fact, in a process of blending and fusing of ideas and ideals (which stands in stark contrast to the dictionary meaning of the term itself), the concept has acquired dozens of additional connotations. They have proved notoriously hard to pin down, to judge by the incongruence of the emotional and poetic reactions they have elicited. Here is a small sample: Purity is obscurity.Ogden Nash One cannot be precise and still be pure. Marc Chagall. Unto the pure all things are pure. New Testament To the pure all things are impure. Mark Twain To the pure all things are indecent. Oscar Wilde ;Blessed are the pure in heart for they have so much more to talk about. Edith Wharton Be thou as chaste as ice, as pure as snow, thou shalt not escape calumny. Get thee to a nunnery, go. W. Shakespeare. Necessary, for ever necessary, to burn out false shames and smelt the heaviest ore of the body into purity. D. H. Lawrence. Necessary, for ever necessary, to burn out false shames and smelt the heaviest ore of the body into purity.D. H. Lawrence. Mathematics possesses not only truth, but supreme beauty - a beauty cold and austere, like that of a sculpture, without appeal to any part of our weaker nature, sublimely pure, and capable of a stern perfection such as only the greatest art can show. Bertrand Russell. Purity strikes me as the most mysterious of the virtues and the more I think about it the less I know about it.Flannery O’Connor.

Subfields: Algebra and Number Theory, Computational Theory and Mathematics, Geometry and Topology

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