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E-raamat: Incidence Algebras [Taylor & Francis e-raamat]

(University of Connecticut, Storrs),
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Teised raamatud teemal:
This work covers the maximal and prime ideals of the incidence algebra, derivations and isomorphisms, radicals and additional ring-theoretic properties. Combinatorial discussions include a study of the Mobius function, reduced incidence subalgebras, and the coalgebra approach to incidence algebras.;College or university bookstores may order five or more copies for a special student price, which is available on request from Marcel Dekker.
Preface iii(6)
List of Figures
ix
1 Incidence Algebras
1(32)
1.1 Partially Ordered Sets
1(8)
1.2 The Incidence Algebra
9(9)
1.3 Subalgebras
18(15)
2 The Mobius Function
33(74)
2.1 The Mobius Function
33(19)
2.2 The Mobius Algebra
52(35)
2.3 Some applications of Mobius Inversion
87(14)
2.4 The Polya-de Bruijn Theorem
101(6)
3 Reduced Incidence Algebras
107(56)
3.1 Generating Functions
107(14)
3.2 The Reduced Incidence Coalgebra
121(20)
3.3 Incidence Hopf Algebras
141(22)
4 Radicals
163(26)
4.1 SomeLattice Theory
163(5)
4.2 The Jacobson Radical
168(5)
4.3 Nil Radicals
173(16)
5 Maximal Ideals
189(28)
5.1 Maximal Ideals of I(X,F)
189(14)
5.2 Maximal Ideals of I(X,R)
203(6)
5.3 Omega Maximal Ideals
209(8)
6 Minimal Prime Ideals
217(34)
6.1 Minimal Prime Ideals of I(X,F)
217(14)
6.2 Some Prime Ideals in I(X,R)
231(9)
6.3 Krull Dimension
240(11)
7 Derivations and Isomorphisms
251(32)
7.1 Derivations
251(8)
7.2 The Isomorphism Problem
259(14)
7.3 Automorphisms
273(10)
8 Ring Theoretic Properties
283(24)
8.1 Rings of Quotients
283(13)
8.2 Polynomial Identities
296(9)
8.3 Additional Remarks
305(2)
List of Symbols
307(10)
Bibliography 317(10)
Index 327
Spiegel\, Eugene; O'Donnell\, Christopher