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On Weak (α, δ)-Compatible Rings

Ouyang Lunqun, Liu Jingwang

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Abstract

For a ring endomorphism α and an α-derivation δ, we introduce the notion of weak (α, δ)-compatible rings, that is a generalization of α-rigid rings and (α, δ)-compatible rings. We first observe the basic properties of weak (α, δ)-compatible rings, and extend the class of weak (α, δ)compatible rings through various ring extensions. We next study on the relationship between the ideal quotient property of the ring R and that of the Ore extension R[x; α, δ] in case R is weak (α, δ)-compatible. Mathematics Subject Classification: 16D25; 16D40

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What this paper is about

For a ring endomorphism α and an α-derivation δ, we introduce the notion of weak (α, δ)-compatible rings, that is a generalization of α-rigid rings and (α, δ)-compatible rings. We first observe the basic properties of weak (α, δ)-compatible rings, and extend the class of weak (α, δ)compatible rings through various ring extensions. We next study on the relationship between the ideal quotient property of the ring R and that of the Ore extension R[x; α, δ] in case R is weak (α, δ)-compatible. Mathematics Subject Classification: 16D25; 16D40

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Available abstract

For a ring endomorphism α and an α-derivation δ, we introduce the notion of weak (α, δ)-compatible rings, that is a generalization of α-rigid rings and (α, δ)-compatible rings. We first observe the basic properties of weak (α, δ)-compatible rings, and extend the class of weak (α, δ)compatible rings through various ring extensions. We next study on the relationship between the ideal quotient property of the ring R and that of the Ore extension R[x; α, δ] in case R is weak (α, δ)-compatible. Mathematics Subject Classification: 16D25; 16D40

Key concepts: Mathematics, Ring (chemistry), Pure mathematics, Generalization, Endomorphism, Ideal (ethics), Property (philosophy), Class (philosophy)

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