Sarah Poiani, University of New Mexico
Authors: Sarah Poiani, Janet Vassilev
2023 AWM Research Symposium
Poster Presentation

In his survey of closure operations, Epstein goes over several constructions which always produce closure operations. Pair operations were introduced by Epstein, R.G. and Vassilev as generalizations of closure and interior operations, but they are so general that they encompass other types of operations that don't behave like closure or interior operations. We will examine constructions for pair operations such as ring extensions, intersections, and unions. Given a collection of pair operations satisfying a specific property, there is no guarantee that the resulting operation will inherit the property. In particular, to obtain an idempotent or involutive pair operation through these constructions often requires additional assumptions on the pair operations in the original collection besides the desired property.

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