This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant’s textbook, __Introduction to Relation Algebras__ (Springer, 2017). "This monograph details several different methods for constructing simple relation algebras, many of which are new with this book. By drawing these seemingly different methods together, all are shown to be aspects of one general approach, for which several applications are given. These tools for constructing and analyzing relation algebras are of particular interest to mathematicians working in logic, algebraic logic, or universal algebra, but will also appeal to philosophers and theoretical computer scientists working in fields that use mathematics. The book is written with a broad audience in mind and features a careful, pedagogical approach; an appendix contains the requisite background material in relation algebras. Over 400 exercises provide ample opportunities to engage with the material, making this a monograph equally appropriate for use in a special topics course or for independent study. Readers interested in pursuing an extended background study of relation algebras will find a comprehensive treatment in author Steven Givant's textbook, Introduction to Relation Algebras (Springer, 2017)"--Back cover Front Matter ....Pages i-xxiv Front Matter ....Pages 1-1 Rectangular Semiproducts (Steven Givant, Hajnal Andréka)....Pages 3-37 Equivalence Semiproducts (Steven Givant, Hajnal Andréka)....Pages 39-63 Front Matter ....Pages 65-69 Diagonal Semiproducts (Steven Givant, Hajnal Andréka)....Pages 71-101 Semipowers (Steven Givant, Hajnal Andréka)....Pages 103-131 Simple Closures (Steven Givant, Hajnal Andréka)....Pages 133-188 Quasi-Bijective Relation Algebras (Steven Givant, Hajnal Andréka)....Pages 189-209 Front Matter ....Pages 211-216 Quotient Relation Algebras and Equijections (Steven Givant, Hajnal Andréka)....Pages 217-261 Quotient Semiproducts (Steven Givant, Hajnal Andréka)....Pages 263-319 Group and Geometric Quotient Semiproducts (Steven Givant, Hajnal Andréka)....Pages 321-406 Front Matter ....Pages 407-410 Insertion Semiproducts (Steven Givant, Hajnal Andréka)....Pages 411-481 Two-Quasi-Bijective Relation Algebras (Steven Givant, Hajnal Andréka)....Pages 483-521 Back Matter ....Pages 523-622
