An overring-theoretic approach to polynomial extensions of star and semistar operations

Details An overring-theoretic approach to polynomial extensions of star and semistar operations An overring-theoretic approach to polynomial extensions of star and semistar operations

2010-04-25

arxiv.org/abs/1004.4369v1

Mathematics

Commutative Algebra

Scientific paper

Call a semistar operation $\ast$ on the polynomial domain $D[X]$ an extension (respectively, a strict extension) of a semistar operation $\star$ defined on an integral domain $D$, with quotient field $K$, if $E^\star = (E[X])^{\ast}\cap K$ (respectively, $E^\star [X]= (E[X])^{\ast}$) for all nonzero $D$-submodules $E$ of $K$. In this paper, 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 $D$.

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