Abstract
Call a semistar operation ⊛ on the polynomial domain D[X] an extension (respectively, a strict extension) of a semistar operation ☆ defined on an integral domain D, with quotient field K, if E ☆ = (E[X])⊛ ∩ K (respectively, E ☆[X] = (E[X])⊛) for all nonzero D-submodules E of K. In this article, we study the general properties of the above defined extensions and link our work with earlier efforts, centered on the stable semistar operation case, at defining semistar operations on D[X] that are “canonical” extensions (or, “canonical” strict extensions) of semistar operations on D.
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have