Arithmetic euclidean rings
Arithmetic functions over rings with zero divisors.
Arithmetic of block monoids
Arithmetic of non-principal orders in algebraic number fields
Let be an order in an algebraic number field. If is a principal order, then many explicit results on its arithmetic are available. Among others, is half-factorial if and only if the class group of has at most two elements. Much less is known for non-principal orders. Using a new semigroup theoretical approach, we study half-factoriality and further arithmetical properties for non-principal orders in algebraic number fields.
Arithmetic progressions in a unique factorization domain
Arithmetical properties of finite rings and algebras, and analytic number theory. III. Finite modules and algebras over Dedekind domains.
Arithmetical quadratic surfaces of genus 0, II.
Artin's conjecture on primes with prescribed primitive roots
Atomicity and the fixed divisor in certain pullback constructions
Let D be an integral domain with field of fractions K. In this article, we use a certain pullback construction in the spirit of Int(E,D) that furnishes many examples of domains between D[x] and K[x] in which there are elements that do not admit a finite factorization into irreducible elements. We also define the notion of a fixed divisor for this pullback construction to characterize all of its irreducible elements and those nonzero nonunits that do admit a finite factorization into irreducibles....
Automata and the arithmetic of formal power series