Polynomial Rings over Pseudovaluation Rings
Copyright policy )Polynomial Rings over Pseudovaluation Rings
LetRbe a ring. Letσbe an automorphism ofR. We define aσ-divided ring and prove the following. (1) LetRbe a commutative pseudovaluation ring such thatx∉Pfor anyP∈Spec(R[x,σ]). ThenR[x,σ]is also a pseudovaluation ring. (2) LetRbe aσ-divided ring such thatx∉Pfor anyP∈Spec(R[x,σ]). ThenR[x,σ]is also aσ-divided ring. Let nowRbe a commutative NoetherianQ-algebra (Qis the field of rational numbers). Letδbe a derivation ofR. Then we prove the following. (1) LetRbe a commutative pseudovaluation ring. ThenR[x,δ]is also a pseudovaluation ring. (2) LetRbe a divided ring. ThenR[x,δ]is also a divided ring.
strongly prime ideals, divided rings, Ordinary and skew polynomial rings and semigroup rings, QA1-939, skew polynomial rings, pseudovaluation rings, Ideals and multiplicative ideal theory in commutative rings, Mathematics, Valuations, completions, formal power series and related constructions (associative rings and algebras), Ideals in associative algebras
strongly prime ideals, divided rings, Ordinary and skew polynomial rings and semigroup rings, QA1-939, skew polynomial rings, pseudovaluation rings, Ideals and multiplicative ideal theory in commutative rings, Mathematics, Valuations, completions, formal power series and related constructions (associative rings and algebras), Ideals in associative algebras
selected citations These citations are derived from selected sources.This is an alternative to the "Influence" indicator, which also reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).0 popularity This indicator reflects the "current" impact/attention (the "hype") of an article in the research community at large, based on the underlying citation network.Average influence This indicator reflects the overall/total impact of an article in the research community at large, based on the underlying citation network (diachronically).Average impulse This indicator reflects the initial momentum of an article directly after its publication, based on the underlying citation network.Average
Citations provided by BIP!Popularity provided by BIP!