We also provide a direct proof of the Grothendieck theorem, which does not ... Then one shows that the set of isomorphism classes of polarized abelian ...
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linkinghub.elsevier.com/retrieve/pii/S0022404903001440
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Proof. The necessity is clear. Since two finite abelian groups of equal order are isomorphic if their Sylow subgroups are isomorphic we may restrict our con ...
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www.jstor.org/stable/2313001
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of Abelian. Groups Without. Torsion. THEOREM 1. Any semi-isomorphism of an Abelian group without torsion of rank r -< 2 is an isomolplrjsmt. Proof. ...
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www.springerlink.com/index/748J0H4MGG4LG517.pdf
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Source: Pacific J. Math. Volume 8, Number 4 (1958), 679-683. ... [1] L. M. Blumenthal, Theory and applicationsof distance geometry, Oxford at the Clarendon Press, 1953. ... [2] I. Kaplansky, Infinite Abelian groups, University of Michigan Press, Ann Arbor, 1954.
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projecteuclid.org/Dienst/Repository/1.0/Disseminate/euc...
projecteuclid.org/Dienst/Repository/1.0/Disseminate/euclid.pjm/1103039693/body/pdf
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The definition of an abelian group is also useful in discussing vector spaces and modules. ... Proof: First, let A be an abelian group isomorphic to Zp, ...
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www.math.niu.edu/~beachy/rings_modules/notes/03.pdf
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locally compact Abelian groups having isometrically isomorphic group ..... Proof. Being open in the totally disconnected group G, B(G) is also open in ...
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journals.cambridge.org/production/action/cjoGetFulltext...
journals.cambridge.org/production/action/cjoGetFulltext?fulltextid=20502
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HomK(R-Mod)(R(X),C); is an isomorphism. Hence C is GS-local. This example generates new ones: let A be a Grothendieck abelian category en-dowed with a functor; U : ... Furthermore, if C is acyclic, then this map is also a quasi-isomorphism. Proof. The pushout square; SnE /; ²; 0; ²; Dn−1E / Sn+1E implies the first...
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www.intlpress.com/HHA/v11/n1/a11/pdf
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K) which are also R-modules (resp. ... X)f. x2 The functor T V Let V be an elementary abelian p-group, ... Proof: The fact that ffl is an isomorphism if M has the stated tensor product * *decompositon follows directly from 2.3(2), 2.5 and [L, 4.2]. Conversely, under the assumpti* *on that ffl is an isomorphism Proposition 2.4 of...
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www.math.purdue.edu/research/atopology/Dwyer-Wilkerson/...
www.math.purdue.edu/research/atopology/Dwyer-Wilkerson/nullmaps/nullmaps.txt
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Abelian variety - Wikipedia, the free encyclopedia
In mathematics, particularly in algebraic geometry, complex analysis and number theory, an abelian variety is a projective algebraic variety that is also an algebraic group, i.e., has a group law th...
en.wikipedia.org/wiki/Abelian_variety
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