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Skew ring extensions and generalized monoid rings

Citation

Cojuhari, EP and Gardner, BJ, Skew ring extensions and generalized monoid rings, Acta Mathematica Hungarica, 154, (2) pp. 343-361. ISSN 0236-5294 (2018) [Refereed Article]

Copyright Statement

2001A8k Akademiai Kaido Budapest, Hungary

DOI: doi:10.1007/s10474-018-0787-x

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 Details

Item Type:Refereed Article
Keywords:skew polynomial ring, skew monoid ring, normalizing extension, subnormalizing extension, graded ring, algebra
Research Division:Mathematical Sciences
Research Group:Pure mathematics
Research Field:Algebra and number theory
Objective Division:Expanding Knowledge
Objective Group:Expanding knowledge
Objective Field:Expanding knowledge in the mathematical sciences
UTAS Author:Gardner, BJ (Dr Barry Gardner)
ID Code:129657
Year Published:2018
Web of Science® Times Cited:2
Deposited By:Mathematics and Physics
Deposited On:2018-12-11
Last Modified:2019-02-27
Downloads:0

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