Displaying similar documents to “Relationship of certain rings of infinite matrices over integers”

Left APP-property of formal power series rings

Zhongkui Liu, Xiao Yan Yang (2008)

Archivum Mathematicum

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A ring R is called a left APP-ring if the left annihilator l R ( R a ) is right s -unital as an ideal of R for any element a ∈ R . We consider left APP-property of the skew formal power series ring R [ [ x ; α ] ] where α is a ring automorphism of R . It is shown that if R is a ring satisfying descending chain condition on right annihilators then R [ [ x ; α ] ] is left APP if and only if for any sequence ( b 0 , b 1 , ⋯ ) of elements of R the ideal l R ( ∑ j = 0 ∞ ∑ k = 0 ∞ R α k ( b j ) ) is right s -unital. As an application we give a sufficient condition under which...

Minimal prime ideals of skew polynomial rings and near pseudo-valuation rings

Vijay Kumar Bhat (2013)

Czechoslovak Mathematical Journal

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Let R be a ring. We recall that R is called a near pseudo-valuation ring if every minimal prime ideal of R is strongly prime. Let now σ be an automorphism of R and δ a σ -derivation of R . Then R is said to be an almost δ -divided ring if every minimal prime ideal of R is δ -divided. Let R be a Noetherian ring which is also an algebra over ℚ ( ℚ is the field of rational numbers). Let σ be an automorphism of R such that R is a σ ( * ) -ring and δ a σ -derivation of R such that σ ( δ ( a ) ) = δ ( σ ( a ) ) for all a ∈ R . Further,...

On a theorem of McCoy

Rajendra K. Sharma, Amit B. Singh (2024)

Mathematica Bohemica

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We study McCoy’s theorem to the skew Hurwitz series ring ( HR , ω ) for some different classes of rings such as: semiprime rings, APP rings and skew Hurwitz serieswise quasi-Armendariz rings. Moreover, we establish an equivalence relationship between a right zip ring and its skew Hurwitz series ring in case when a ring R satisfies McCoy’s theorem of skew Hurwitz series.