5) the second Helly theorem Helly第二定理6) isomorphism theorem 同构定理 1. This paper investigates the properties of quotient spaces and obtains the first, second isomorphism theorems and homomorphism foundamental theorem. 研究了商空间的性质,给出了有关商空间的第一、第二同构定理和同态基本定理...
Basic Algebr a II Second Editio n N A T H A N J A C O B S O N YAL E UNIVERSIT Y • B W . H . F R E E M A N A N D C O M P A N Y N ew Yor k To Mik e and Polly Library of Congress Cataloging-in-Publication Data (Revised for vol. 2) Jacobson, Nathan, ...
Proof of Theorem 5. We have seen that if 𝑿⊗𝒀X⊗Y is regular of dimension 1, then 𝝀λ is an isomorphism. On the other hand, assume that 𝝀λ is surjective. Then, by the exact sequence in Proposition 6, we see that ∧𝟐(Ω𝟏(𝑿⊗𝒀))=𝟎.∧2(Ω1(X⊗Y...