Andre Leroy - Böcker

This book contains the proceedings of the Fifth International Conference on Noncommutative Rings and their Applications, held from June 12-15, 2017, at the University of Artois, Lens, France.The papers are related to noncommutative rings, covering topics such as: ring theory, with both the elementwise and more structural approaches developed; module theory with popular topics such as automorphism invariance, almost injectivity, ADS, and extending modules; and coding theory, both the theoretical aspects such as the extension theorem and the more applied ones such as Construction A or Reed-Muller codes. Classical topics like enveloping skewfields, weak Hopf algebras, and tropical algebras are also presented.

This volume contains the proceedings of two conferences: NonCommutative Rings and their Applications (NCRA, VIII) and Quadratic Forms, Rings and Codes (QFRC II) that were held in August 2023 at Artois University, Lens, France. The book contains a few survey papers and many research articles. The latter have been written in an accessible style and should be of interest to specialists, researchers, and graduate students. The subjects cover classical ring theory (e.g. Baer rings, separativity problem, group algebras, quasi-duo) coding theory (MacWilliams identities, codes over Galois rings or from Lie algebras). Quadratic forms are also present in two important and nicely written papers. Finally, some papers offer new perspectives moving from classical ring theory to universal algebras and non-associative structures.