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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:	https://doi.org/10.1007/s10474-018-0787-x
Copyright Information:	© 2001A8k Akademiai Kaido Budapest, Hungary
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