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Skew ring extensions and generalized monoid rings

Cojuhari, EP and Gardner, BJ 2018 , 'Skew ring extensions and generalized monoid rings' , Acta Mathematica Hungarica, vol. 154, no. 2 , pp. 343-361 , doi: 10.1007/s10474-018-0787-x.

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Abstract

A D-structure on a ring A with identity is a family of self-mappings indexed by the elements of a monoid G and subject to a long list of rather natural conditions. The mappings are used to define a generalization of the monoid algebra A[G]. We consider two of the simpler types of D-structure. The first is based on a homomorphism from G to End(A) and leads to a skew monoid ring. We also explore connections between these D-structures and normalizing and subnormalizing extensions. The second type of D-structure considered is built from an endomorphism of A. We use D-structures of this type to characterize rings which can be graded by a cyclic group of order 2.

Item Type: Article
Authors/Creators:Cojuhari, EP and Gardner, BJ
Keywords: skew polynomial ring, skew monoid ring, normalizing extension, subnormalizing extension, graded ring, algebra
Journal or Publication Title: Acta Mathematica Hungarica
Publisher: Akademiai Kiado
ISSN: 0236-5294
DOI / ID Number: 10.1007/s10474-018-0787-x
Copyright Information:

© 2001A8k Akademiai Kaido Budapest, Hungary

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