منابع مشابه
Purity of Methods
ly considered from such construction; and which doth accompany it though otherwise constructed than is supposed.7 Wallis thus saw geometrical knowledge as more concerned with construction-invariant features of geometrical figures than with features deriving from their construction. In addition, he saw algebraic 5. Idem, p. 230 6. Knowing via minimal or simplest cause would have been better stil...
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We investigate pure monomorphisms and pure epimorphisms in varieties of universal algebras with applications to equationally compact (= pure injective) algebras, pure projective algebras and perfect varieties.
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Let R be a regular local ring, K its field of fractions and A1, A2 two Azumaya algebras with involutions over R. We show that if A1 ⊗R K and A1 ⊗R K are isomorphic over K, then A1 and A2 are isomorphic over R. In particular, if two quadratic spaces over the ring R become similar over K then these two spaces are similar already over R. The results are consequences of a purity theorem for similar...
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— GROTHENDIECK'S absolute cohomological purity conjecture is proved for Q7-etale cohomology, and for etale cohomology with 7.1 f coefficients if / is large. The proof depends on Quillen's localization theorem for algebraic K-thcory and my comparison of algebraic and topological X-thcory. In this note, I show how my theorem relating algebraic and topological K-theory yields an absolute cohomolog...
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We show that if a class of modules is closed under pure quotients, then it is precovering if and only if it is covering, and this happens if and only if it is closed under direct sums. This is inspired by a dual result by Rada and Saorín. We also show that if a class of modules contains the ground ring and is closed under extensions, direct sums, pure submodules, and pure quotients, then it for...
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ژورنال
عنوان ژورنال: Excursions Journal
سال: 2020
ISSN: 2044-4095,2055-494X
DOI: 10.20919/exs.10.2020.302