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- W3075399328 abstract "Abstract The subject of the paper is suggested by G. Janelidze and motivated by his earlier result giving a positive answer to the question posed by S. MacLane whether the Galois theory of homogeneous linear ordinary differential equations over a differential field (which is Kolchin–Ritt theory and an algebraic version of Picard–Vessiot theory) can be obtained as a particular case of G. Janelidze’s Galois theory in categories. One ground category in the Galois structure involved in this theory is dual to the category of commutative rings with unit, and another one is dual to the category of commutative differential rings with unit. In the present paper, we apply the general categorical construction, the particular case of which gives this Galois structure, by replacing “commutative rings with unit” by algebras from any variety <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=script>V</m:mi> </m:math> mathscr{V} of universal algebras satisfying the amalgamation property and a certain condition (of the syntactical nature) for elements of amalgamated free products which was introduced earlier, and replacing “commutative differential rings with unit” by <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=script>V</m:mi> </m:math> mathscr{V} -algebras equipped with additional unary operations which satisfy some special identities to construct a new Galois structure. It is proved that this Galois structure is admissible. Moreover, normal extensions with respect to it are characterized in the case where <m:math xmlns:m=http://www.w3.org/1998/Math/MathML> <m:mi mathvariant=script>V</m:mi> </m:math> mathscr{V} is any of the following varieties: abelian groups, loops and quasigroups." @default.
- W3075399328 created "2020-08-24" @default.
- W3075399328 creator A5043142279 @default.
- W3075399328 date "2020-08-04" @default.
- W3075399328 modified "2023-09-24" @default.
- W3075399328 title "Admissible Galois Structures on the categories dual to some varieties of universal algebras" @default.
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- W3075399328 doi "https://doi.org/10.1515/gmj-2020-2073" @default.
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