Contributions to Universal Algebra

B. Csákány, J. Schmidt

• Publisher: North Holland
• Year: 2014
• Print ISBN: 9780720407259
• eBook ISBN: 9781483103020
• Topic: Mathematics
• Subtopic: Algebra
• Index: Mathematics

Contributions to Universal Algebra focuses on the study of algebra. The compilation first discusses the congruence lattice of pseudo-simple algebras; elementary properties of limit reduced powers with applications to Boolean powers; and congruent lattices of 2-valued algebras. The book further looks at duality for algebras; weak homomorphisms of stone algebras; varieties of modular lattices not generated by their finite dimensional members; and remarks on algebraic operations of stone algebras. The text describes polynomial normal forms and the embedding of polynomial algebras; coverings in the lattice of varieties; embedding semigroups in semigroups generated by idempotents; and endomorphism semigroups and subgroupoid lattices. The book also discusses a report on sublattices of a free lattice, and then presents the cycles in finite semi-distributive lattices; cycles in S-lattices; and summary of results. The text also describes primitive subsets of algebras, ideals, normal sets, and congruences, as well as Jacobson's density theorem. The book is a good source for readers wanting to study algebra.

Table of contents

• Front Cover
• Contributions to Universal Algebra
• Copyright Page
• PREFACE
• CONTENTS
• LIST OF PARTICIPANTS
• Chapter 1. ON THE CONGRUENCE LATTICE OF PSEUDO-SIMPLE ALGEBRAS
• Chapter 2. ELEMENTARY PROPERTIES OF LIMIT REDUCED POWERS WITH APPLICATIONS TO BOOLEAN POWERS
• Chapter 3. ON CONGRUENCE LATTICES OF 2-VALUED ALGEBRAS
• Chapter 4. THE c-IDEAL LATTICE AND SUBALGEBRA LATTICE ARE INDEPENDENT
• Chapter 5. /-GROUP-CONE AND BOOLEAN ALGEBRA. A COMMON ONE-IDENTITY-AXIOM
• Chapter 6. SPLITTING LATTICES AND CONGRUENCE MODULARITY*
• Chapter 7. SOME REMARKS ON WEAK AUTOMORPHISMS
• Chapter 8. ON POLYNOMIAL ALGEBRAS
• Chapter 9. DUALITY FOR ALGEBRAS
• Chapter 10. PROJECTIVE AND INJECTIVE VARIETIES OF ABELIAN Ω-ALGEBRAS
• Chapter 11. SOME VARIETIES OF MODULAR LATTICES NOT GENERATED BY THEIR FINITE DIMENSIONAL MEMBERS
• Chapter 12. ON WEAK HOMOMORPHISMS OF STONE ALGEBRAS
• Chapter 13. ON THE SUMS OF DOUBLE SYSTEMS OF LATTICES AND DS-CONGRUENCES OF LATTICES
• Chapter 14. n-DISTRIBUTIVITY AND SOME QUESTIONS OF THE EQUATIONAL THEORY OF LATTICES
• Chapter 15. POLYNOMIAL NORMAL FORMS AND THE EMBEDDING OF POLYNOMIAL ALGEBRAS
• Chapter 16. COVERINGS IN THE LATTICE OF VARIETIES
• Chapter 17. EMBEDDING SEMIGROUPS IN SEMIGROUPS GENERATED BY IDEMPOTENTS
• Chapter 18. ENDOMORPHISM SEMIGROUPS AND SUBGROUPOID LATTICES
• Chapter 19. A NOTE ON IMPLICATIONAL SUBCATEGORIES
• Chapter 20. A REPORT ON SUBLATTICES OF A FREE LATTICE
• Chapter 21. EXTENSIVE GROUPOID VARIETIES
• Chapter 22. PRIMITIVE SUBSETS OF ALGEBRAS
• Chapter 23. IDEALS, NORMAL SETS AND CONGRUENCES
• Chapter 24. A CHARACTERIZATION OF COMPLETE MODULAR p-ALGEBRAS
• Chapter 25. JACOBSON'S DENSITY THEOREM IN UNIVERSAL ALGEBRA
• Chapter 26. CERTAIN QUESTIONS OF THE THEORY OF HOMOTOPY OF UNIVERSAL ALGEBRAS
• Chapter 27. A THEOREM ON FINITE SUBLATTICES OF FREE LATTICES
• Chapter 28. A NOTE ON A PROBLEM OF GORALČÍK
• Chapter 29. QUASI-DECOMPOSITIONS, EXACT SEQUENCES, AND TRIPLE SUMS OF SEMIGROUPS. I. GENERAL THEORY
• Chapter 30. QUASI-DECOMPOSITIONS, EXACT SEQUENCES, AND TRIPLE SUMS OF SEMIGROUPS. II. APPLICATIONS
• Chapter 31. ENDOMORPHICALLY COMPLETE GROUPS
• Chapter 32. CONCRETE CATEGORIES WITH NON-INJECTIVE MONOMORPHISM
• Chapter 33. ON ALGEBRAS AS TREE AUTOMATA
• Chapter 34. ON AFFINE MODULES
• Chapter 35. EQUATIONAL LOGIC
• Chapter 36. ON REGULAR ALGEBRAS
• Chapter 37. REMARKS ON FULLY INVARIANT CONGRUENCES
• Chapter 38. VARIETIES GENERATED BY QUASI-PRIMAL ALGEBRAS HAVE DECIDABLE THEORIES
• Chapter 39. ON THE POLYNOMIAL COMPLETENESS DEFECT OF UNIVERSAL ALGEBRAS
• Chapter 40. ON LATTICES FREELY GENERATED BY FINITE PARTIALLY ORDERED SETS
• Chapter 41. PROPER AND IMPROPER FREE ALGEBRAS
• PROBLEMS