10 citations · 13 across the 13 of their papers we have counts for
6 papers · 1 filter
Semistar operations on Dedekind domains
Jesse Elliott
We give an explicit description of the lattice $\Semistar(D)$ of all semistar operations on any Dedekind domain from its set $\Max(D)$ of maximal ideals. This descpription is c…
Presentations and module bases of integer-valued polynomial rings
Jesse Elliott
Let D be an integral domain with quotient field K. For any set X, the ring Int(D^X) of integer-valued polynomials on D^X is the set of all polynomials f in K[X] such that f(D^X) is…
Birings and plethories of integer-valued polynomials
Jesse Elliott
Let and be commutative rings with identity. An {\it --biring} is an -algebra together with a lift of the functor from -algebras to sets to a fu…
Factoring formal power series over principal ideal domains
Jesse Elliott
We provide an irreducibility test and factoring algorithm (with some qualifications) for formal power series in the unique factorization domain , where is any principal…
Integer-valued polynomials, -closure, and associated primes
Jesse Elliott
Given an integral domain with quotient field , the ring of integer-valued polynomials on D is the subring of the polynomial ring .…
Prequantales and applications to semistar operations and module systems
Jesse Elliott
We show that a generalization of quantales and prequantales provides a noncommutative and nonassociative abstract ideal theoretic setting for the theories of star operations, semis…