Algebraic Structure of Knot Modules by J. P. Levine

By J. P. Levine

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2. submodules, l it will suffice is a power of a single prime A n o t h e r r e s t r i c t i o n we will make concerns A/(n), i -th 7- if and only if all of the other prime are coprime to A are the lower and upper Recall that for large enough In this case prime A. Ai, A i R. the structure of the In order to extract invariants and consider c l a s s i f i c a t i o n questions, we is a D e d e k i n d domain. A is Dedekind if the domain is a domain, R = A/(n) then an irreducible element is a Dedekind domain.

Submodules, l it will suffice is a power of a single prime A n o t h e r r e s t r i c t i o n we will make concerns A/(n), i -th 7- if and only if all of the other prime are coprime to A are the lower and upper Recall that for large enough In this case prime A. Ai, A i R. the structure of the In order to extract invariants and consider c l a s s i f i c a t i o n questions, we is a D e d e k i n d domain. A is Dedekind if the domain is a domain, R = A/(n) then an irreducible element is a Dedekind domain.

For this assumptions projective to p r o v e B I. i (**)--except Now -~ A k "* 0 the e x a c t n e s s is zero . 0 II Ai÷l construction of d i a g r a m Ak * the maps that + Ak + ~ > Bi÷l row are i < k - i, position ÷ Ai + ¢i+t the b o t t o m according + Bi+l of the the + Ai+l that is the p r o p e r t y during and we may, its top are an e x e r c i s e top row fact the is i m p l i e d the comof ¢i construction. therefore, split 31 Ai Furthermore, if we a splitting A0 ÷ A1 + follows maps for Ci ÷ Bi Ai (**) to o b t a i n Furthermore The on straightforward, Corollary q-only and torsion, ~ e A B = Ker ~ k .

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