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Skew ring extensions and generalized monoid rings
journal contributionposted on 2023-05-19, 23:06 authored by Cojuhari, EP, Barry GardnerBarry Gardner
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.
Publication titleActa Mathematica Hungarica
Department/SchoolSchool of Natural Sciences
Place of publicationPo Box 245, Budapest, Hungary, H-1519
Rights statement© 2001A8k Akademiai Kaido Budapest, Hungary