Advances in Commutative Algebra

AYMAN BADAWI is Professor at the Department of Mathematics and Statistics, the American University of Sharjah, the United Arab Emirates. He earned his Ph.D. in Algebra from the University of North Texas, USA, in 1993. He is an active member of the American Mathematical Society and honorary member of the Middle East Center of Algebra and its Applications. His research interests include commutative algebra, pi-regular rings, and graphs associated to rings. JIM COYKENDALL is Professor of Mathematical Sciences at Clemson University, South Carolina, USA. He earned his Ph.D. from Cornell University in 1995, and has held various academic positions at the California Institute of Technology, the University of Tennessee, Cornell University, Lehigh University, and North Dakota State University. He has successfully guided 12 Ph.D. students. His research interests include commutative algebra and number theory.

Chapter 1. Strongly Divided Pairs of Integral Domains.- Chapter 2. Strongly Additively Regular Rings and Graphs.- Chapter 3. Intersections of Prufer Overrings.- Chapter 4. A Survey of David Anderson’s Mathematical Works.- Chapter 5. Isomorphisms of Zero-Divisor Graphs.- Chapter 6. On t-Reductions and t-Integral Closure of Ideals in Integral Domains.- Chapter 7. David Anderson’s Work on Graded Integral Domains.- Chapter 8. x-Divisor Pseudographs and Isotopy Invariants of Commutative Quasigroups.- Chapter 9. Local Types of Classical Rings.- Chapter 10. How Elements Really Factor In Z.- Chapter 11. t-Local Domains and Valuation Domains.