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arXiv · 1404.3570

Some topological considerations on semistar operations

C. A. Finocchiaro·D. Spirito
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Abstract

We consider properties and applications of a new topology, called the Zariski topology, on the space ${\rm SStar}(A)$ of all the semistar operations on an integral domain $A$. We prove that the set of all overrings of $A$, endowed with the classical Zariski topology, is homeomorphic to a subspace of ${\rm SStar}(A)$. The topology on ${\rm SStar}(A)$ provides a general theory, through which we see several algebraic properties of semistar operation as very particular cases of our construction. Moreover, we show that the subspace ${\rm SStar}_f(A)$ of all the semistar operations of finite type on $A$ is a spectral space.

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C. A. Finocchiaro, D. Spirito. 2014-04-14. Some topological considerations on semistar operations. https://doi.org/10.1016/j.jalgebra.2014.04.002

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