This book presents a graduate-level course on modern algebra. It can be used as a teaching book
- owing to the copious exercises - and as a source book for those who wish to use the major
theorems of algebra. The course begins with the basic combinatorial principles of algebra:
posets chain conditions Galois connections and dependence theories. Here the general
Jordan-Holder Theorem becomes a theorem on interval measures of certain lower semilattices.
This is followed by basic courses on groups rings and modules the arithmetic of integral
domains fields the categorical point of view and tensor products. Beginning with
introductory concepts and examples each chapter proceeds gradually towards its more complex
theorems. Proofs progress step-by-step from first principles. Many interesting results reside
in the exercises for example the proof that ideals in a Dedekind domain are generated by at
most two elements. The emphasis throughout is on real understanding as opposed to memorizing a
catechism and so some chapters offer curiosity-driven appendices for the self-motivated
student.
