There is, I think, something ethereal about i —the square root of minus one. I remember first hearing about it at school. It seemed an odd beast at that time—an intruder hovering on the edge of reality.

Usually familiarity dulls this sense of the bizarre, but in the case of i it was the reverse: over the years the sense of its surreal nature intensified. It seemed that it was impossible to write mathematics that described the real world in …

I and i

http://web.thu.edu.tw/wang/www/comm_alg/livingston.pdf

The Zero-Divisor Graph of a Commutative Ring☆

Table of basic properties Notation and basic definitions Preface 1. What is the integral closure 2. Integral closure of rings 3. Separability 4. Noetherian rings 5. Rees algebras 6. Valuations 7. Derivations 8. Reductions 9. Analytically unramified rings 10. Rees valuations 11. Multiplicity and integral closure 12. The conductor 13. The Briancon-Skoda theorem 14. Two-dimensional regular local rings 15. Computing the integral closure 16. Integral dependence of modules 17. Joint reductions 18. Adjoints of ideals 19. Normal homomorphisms Appendix A. Some background material Appendix B. Height and dimension formulas References Index.

/pdf/integral-closure-of-ideals-rings-and-modules-3is4mdcjqf.pdf

Integral closure of ideals, rings, and modules

/pdf/infinite-abelian-groups-2dvcz0046a.pdf

Infinite Abelian Groups

This paper introduced the concept of a partial geometry, which serves to unify and generalize certain theorems on embedding of nets, and uniqueness of association schemes of partially balanced designs, by Bruck, Connor, Shrikhande and others. Certain lemmas and theorems are direct generalizations of those proved by Bruck ;-57, for the case of nets, which are a special class of partial geometries.

/pdf/strongly-regular-graphs-partial-geometries-and-partially-28uiebrlxn.pdf

Strongly regular graphs, partial geometries and partially balanced designs.

Multiplicative ideal theory

"Commutative Semigroup Rings" was the first exposition of the basic properties of semigroup rings. Gilmer concentrates on the interplay between semigroups and rings, thereby illuminating both of these important concepts in modern algebra.

Commutative Semigroup Rings

/pdf/overrings-and-divisorial-ideals-of-rings-of-the-form-d-m-33rmkfrv1s.pdf

Overrings and divisorial ideals of rings of the form $D+M$.

/pdf/divisibility-properties-in-semigroup-rings-vo07qhpmk6.pdf

Robert Gilmer

Papers

Multiplicative ideal theory

Commutative Semigroup Rings

Overrings and divisorial ideals of rings of the form $D+M$.

Divisibility properties in semigroup rings.

Overrings of Prüfer domains. II