The q-theory of Finite Semigroups

1. Part I The q operator and Pseudovarieties of Relational Morphisms

2. Foundations for Finite Semigroup Theory
John Rhodes, Benjamin Steinberg

3. The q-operator
John Rhodes, Benjamin Steinberg

4. The Equational Theory
John Rhodes, Benjamin Steinberg

2. Part II Complexity in Finite Semigroup Theory

5. The Complexity of Finite Semigroups
John Rhodes, Benjamin Steinberg

6. Two-Sided Complexity and the Complexity of Operators
John Rhodes, Benjamin Steinberg

3. Part III The Algebraic Lattice of Semigroup Pseudovarieties

7. Algebraic Lattices, Continuous Lattices and Closure Operators
John Rhodes, Benjamin Steinberg

8. The Abstract Spectral Theory of PV
John Rhodes, Benjamin Steinberg

4. Part IV Quantales Idempotent Semirings Matrix Algebras and the Triangular Product

9. Quantales
John Rhodes, Benjamin Steinberg

10. The Triangular Product and Decomposition Results for Semirings
John Rhodes, Benjamin Steinberg

Keywords: Mathematics, Mathematical Logic and Formal Languages, General Algebraic Systems, Order, Lattices, Ordered Algebraic Structures, Group Theory and Generalizations