This volume has been curated from two sources: presentations from the Conference on Rings and Polynomials, Technische Universit?t Graz, Graz, Austria, July 19 24, 2021, and papers intended for presentation at the Fourth International Meeting on Integer-valued Polynomials and Related Topics, CIRM, Luminy, France, which was cancelled due to the pandemic. The collection ranges widely over the algebraic, number theoretic and topological aspects of rings, algebras and polynomials. Two areas of particular note are topological methods in ring theory, and integer valued polynomials. The book is dedicated to the memory of Paul-Jean Cahen, a coauthor or research collaborator with some of the conference participants and a friend to many of the others. This collection contains a memorial article about Paul-Jean Cahen, written by his longtime research collaborator and coauthor Jean-Luc Chabert.
Paul-Jean Cahen (1946 2019) (Chabert).- Bhargavas exponential functions and Bernoulli numbers associated to the set of prime numbers (Adam).- Polynomial root extensions (Anderson).- Absorbing ideals in commutative rings: A survey(Badawi).- Complement-finite ideals (Baeth).- When is a group algebra antimatter? (Baghdadi).- Yosida, Mart?nez, and A + B rings (Klingler).- Functional identities and maps preserving two-sided zero products (Breaar).- Bounded factorization and the ascending chain condition on principal ideals in generalized power series rings (Mooney).- Probabilities and fixed divisors of integer polynomials (Chabert).- Modules over trusses vs. modules over rings: Internal direct sums (Ferdania).- A survey on essential-like properties of Pr?fer v--multiplication domains (Tartarone).- On the subatomicity of polynomial semidomains (Gotti).- Invertibility, semistar operations, and thel{
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