Skew ring extensions and generalized monoid rings

Cojuhari, E. P.; Gardner, B. J.

doi:10.1007/s10474-018-0787-x

Acta Math. Hungar.

2018

DOI: 10.1007/s10474-018-0787-x

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Skew ring extensions and generalized monoid rings

E. P. Cojuhari

B. J. Gardner

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“…[21]). In [7,8,9] Cojuhari and Gardner introduced skew versions R[G; π] of monoid rings in the following sense. Let G denote a monoid with identity element e. For all a, b ∈ G, let π a b : R → R be a function.…”

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confidence: 99%

Simplicity of Ore monoid rings

2019

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Given a non-associative unital ring R, a monoid G and a set π of additive maps R → R, we introduce the Ore monoid ring R[π; G], and, in a special case, the differential monoid ring. We show that these structures generalize, in a natural way, not only the classical Ore extensions and differential polynomial rings, but also the constructions, introduced by Cojuhari, defined by so-called D-structures π. Moreover, for commutative monoids, we give necessary and sufficient conditions for differential monoid rings to be simple. We use this in a special case to obtain new and shorter proofs of classical simplicity results for differential polynomial rings in several variables previously obtained by Voskoglou and Malm by other means. We also give examples of new Ore-like structures defined by finite commutative monoids.

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Simplicity of Ore monoid rings

2019

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Derivations of skew Ore polynomial semirings

Vladeva

2020

Communications in Algebra

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Skew ring extensions and generalized monoid rings

Cited by 2 publications

References 6 publications

Simplicity of Ore monoid rings

Simplicity of Ore monoid rings

Derivations of skew Ore polynomial semirings

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