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arXiv · 2302.00238

How to extend closure and interior operations to more modules

Neil Epstein·Rebecca R. G.·Janet Vassilev
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Abstract

There are several ways to convert a closure or interior operation to a different operation that has particular desirable properties. In this paper, we axiomatize 3 ways to do so, drawing on disparate examples from the literature, including tight closure, basically full closure, and various versions of integral closure. In doing so, we explore several such desirable properties, including *hereditary*, *residual*, and *cofunctorial*, and see how they interact with other properties such as the *finitistic* property.

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Neil Epstein, Rebecca R. G., Janet Vassilev. 2023-02-01. How to extend closure and interior operations to more modules. https://doi.org/10.1017/nmj.2023.36

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