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A remark on power series rings.

Paul M. Cohn (1992)

Publicacions Matemàtiques

A trivializability principle for local rings is described which leads to a form of weak algorithm for local semifirs with a finitely generated maximal ideal whose powers meet in zero.

A unified approach to the Armendariz property of polynomial rings and power series rings

Tsiu-Kwen Lee, Yiqiang Zhou (2008)

Colloquium Mathematicae

A ring R is called Armendariz (resp., Armendariz of power series type) if, whenever ( i 0 a i x i ) ( j 0 b j x j ) = 0 in R[x] (resp., in R[[x]]), then a i b j = 0 for all i and j. This paper deals with a unified generalization of the two concepts (see Definition 2). Some known results on Armendariz rings are extended to this more general situation and new results are obtained as consequences. For instance, it is proved that a ring R is Armendariz of power series type iff the same is true of R[[x]]. For an injective endomorphism σ of a ring...

Abelian modules.

Agayev, N., Güngöroğlu, G., Harmanci, A., Halicioğlu, S. (2009)

Acta Mathematica Universitatis Comenianae. New Series

An intermediate ring between a polynomial ring and a power series ring

M. Tamer Koşan, Tsiu-Kwen Lee, Yiqiang Zhou (2013)

Colloquium Mathematicae

Let R[x] and R[[x]] respectively denote the ring of polynomials and the ring of power series in one indeterminate x over a ring R. For an ideal I of R, denote by [R;I][x] the following subring of R[[x]]: [R;I][x]: = i 0 r i x i R [ [ x ] ] : ∃ 0 ≤ n∈ ℤ such that r i I , ∀ i ≥ n. The polynomial and power series rings over R are extreme cases where I = 0 or R, but there are ideals I such that neither R[x] nor R[[x]] is isomorphic to [R;I][x]. The results characterizing polynomial rings or power series rings with a certain ring...

Central Armendariz rings.

Agayev, Nazim, Güngöroğlu, Gonca, Harmanci, Abdullah, Halicioğlu, S. (2011)

Bulletin of the Malaysian Mathematical Sciences Society. Second Series

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