On partial Galois abelian extensions
Andr\'es Ca\~nas, V\'ictor Mar\'in, and H\'ector Pinedo
TL;DR
This paper introduces the Harrison partial inverse semigroup, a new algebraic structure that classifies partial Galois abelian extensions of a commutative ring with a fixed group G.
Contribution
It constructs the inverse semigroup of equivalence classes of partial Galois abelian extensions, providing a novel algebraic framework for their classification.
Findings
Defines the Harrison partial inverse semigroup.
Establishes its algebraic properties.
Connects it to partial Galois theory.
Abstract
In this article we construct the inverse semigroup of equivalence classes of partial Galois abelian extensions of a commutative ring R with same group G, called the Harrison partial inverse semigroup.
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Taxonomy
TopicsAlgebraic Geometry and Number Theory · Commutative Algebra and Its Applications · Algebraic structures and combinatorial models