Incidence Algebras: Spiegel; Eugene: 9780824700362: Book: Technology: eCampus.com

Presents many properties of the incidence algebra of a locally finite partially ordered set X over a ring R - focusing specifically on the case when R is a cummutative ring with identity and detailing various properties of the Mobius function. DLC: Incidence algebras.

Preface

iii

(6)

List of Figures

1 Incidence Algebras

(32)

1.1 Partially Ordered Sets

(8)

1.2 The Incidence Algebra

(9)

1.3 Subalgebras

(15)

2 The Mobius Function

(74)

2.1 The Mobius Function

(19)

2.2 The Mobius Algebra

(35)

2.3 Some applications of Mobius Inversion

(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


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