On Euclidean ideal classes in certain Abelian extensions
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DOI: 10.1007/s00209-019-02434-2
Abstract: In this article, we show that certain abelian extensions K with unit rank greater than or equal to three have cyclic class group if and only if it has a Euclidean ideal class. This result… read more here.
Keywords: abelian extensions; euclidean ideal; ideal classes; certain abelian ... See more keywords
The commutative inverse semigroup of partial abelian extensions
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DOI: 10.1080/00927872.2021.1984495
Abstract: This paper is a new contribution to the partial Galois theory of groups. First, given a unital partial action $\alpha_G$ of a finite group $G$ on an algebra $S$ such that $S$ is an $\alpha_G$-partial… read more here.
Keywords: abelian extensions; commutative inverse; inverse semigroup; extensions commutative ... See more keywords
Wells sequences for abelian extensions of Lie coalgebras
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DOI: 10.1142/s0219498821501498
Abstract: For a Lie comodule M of a Lie coalgebra C and the Lie algebra ????(C,M) (respectively, the group ????(C,M)) of diagonal coderivations (respectively, Lie coalgebra automorphisms) of the semidirect sum C ⋉... read more here.
Keywords: abelian extensions; sequences abelian; wells sequences; lie coalgebras ... See more keywords
On a Lie Algebraic Approach to Abelian Extensions of Associative Algebras
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DOI: 10.4153/s0008439520000193
Abstract: Abstract By using a representation of a Lie algebra on the second Hochschild cohomology group, we construct an obstruction class to extensibility of derivations and a short exact sequence of Wells type for an abelian… read more here.
Keywords: extensions associative; approach abelian; abelian extensions; algebraic approach ... See more keywords