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computation of the Hall coefficient g(q)[('6,4,2)(,42)(,4,2)]
 Date Issued:
 2005
 Summary:
 Let L be a uniserial ring of length n, with maximal ideal r , and finite residue field Λ/ r . We consider Λmodules which possess a finite composition series. We note that a Λmodule has the form B ≅ ⨁i=1m Λ/ rli , where the type of B is the partition l = ( l1,&ldots;,lm ) denoted by t(B). For Λmodules A, B, C with t(A) = m , t(B) = l , t(C) = n , if A ⊆ B, and B/A ≅ C, we define GBAC = {U ⊆ B : U ≅ A and B/U ≅ C}. We show that GBAC = MonoA,B,C Aut A =  S (A, B, C)/∼ = glmn (q), where Λ/ r  = q, and the last equality comes from evaluating the Hall polynomial glmn (t) ∈ Z [t] at q, as stated in Hall's Theorem. We note that GBAC make up the coefficients of the Hall algebra. We provide a proof that the Hall algebra is a commutative and associative ring. Using the property of associativity of the Hall algebra and I. G. MacDonald's formula: glb1l =qnl nbn 1li≥ 1l'i b'i,b' il'i+1 q1 we develop a procedure to generate arbitrary Hall polynomials and we compute g6,4,2 4,24,2 (q).
Title:  A computation of the Hall coefficient g(q)[('6,4,2)(,42)(,4,2)]. 
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Name(s): 
Anez, Myriam T. Florida Atlantic University, Degree grantor Schmidmeier, Markus, Thesis advisor 

Type of Resource:  text  
Genre:  Electronic Thesis Or Dissertation  
Issuance:  monographic  
Date Issued:  2005  
Publisher:  Florida Atlantic University  
Place of Publication:  Boca Raton, Fla.  
Physical Form:  application/pdf  
Extent:  123 p.  
Language(s):  English  
Summary:  Let L be a uniserial ring of length n, with maximal ideal r , and finite residue field Λ/ r . We consider Λmodules which possess a finite composition series. We note that a Λmodule has the form B ≅ ⨁i=1m Λ/ rli , where the type of B is the partition l = ( l1,&ldots;,lm ) denoted by t(B). For Λmodules A, B, C with t(A) = m , t(B) = l , t(C) = n , if A ⊆ B, and B/A ≅ C, we define GBAC = {U ⊆ B : U ≅ A and B/U ≅ C}. We show that GBAC = MonoA,B,C Aut A =  S (A, B, C)/∼ = glmn (q), where Λ/ r  = q, and the last equality comes from evaluating the Hall polynomial glmn (t) ∈ Z [t] at q, as stated in Hall's Theorem. We note that GBAC make up the coefficients of the Hall algebra. We provide a proof that the Hall algebra is a commutative and associative ring. Using the property of associativity of the Hall algebra and I. G. MacDonald's formula: glb1l =qnl nbn 1li≥ 1l'i b'i,b' il'i+1 q1 we develop a procedure to generate arbitrary Hall polynomials and we compute g6,4,2 4,24,2 (q).  
Identifier:  9780542385704 (isbn), 13289 (digitool), FADT13289 (IID), fau:10141 (fedora)  
Collection:  FAU Electronic Theses and Dissertations Collection  
Note(s): 
Charles E. Schmidt College of Science Thesis (M.S.)Florida Atlantic University, 2005. 

Subject(s): 
Mathematical statistics Algebra, Abstract Abelian groups 

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Persistent Link to This Record:  http://purl.flvc.org/fcla/dt/13289  
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Host Institution:  FAU  
Is Part of Series:  Florida Atlantic University Digital Library Collections. 