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Let $R$ be a commutative ring with an identity different from zero and $n$ be a positive integer. Anderson and Badawi, in their paper on $n$ -absorbing ideals, define a proper ideal $I$ of a commutative ring $R$ to be an $n$ -absorbing ideal of $R$ , if whenever $x_{1} \dots x_{n + 1} \in I$ for $x_{1}, ..., x_{n + 1} \in R$ , then there are $n$ of the $x_{i}$ ’s whose product is in $I$ and conjecture that $ω_{R [X]} (I [X]) = ω_{R} (I)$ for any ideal $I$ of an arbitrary ring $R$ , where $ω_{R} (I) = min {n : I is an n -absorbing ideal of R}$ . In the present paper, we use content formula techniques to prove that their conjecture is true, if one of the following conditions...

On the construction of explicit solutions to the matrix equation $X^{2} A X = A X A$ .

Li, Aihua, Mosteig, Edward (2010)

ELA. The Electronic Journal of Linear Algebra [electronic only]

On the formal inverse of polynomial endomorphisms

Piotr Ossowski (1998)

Colloquium Mathematicae

On the generalization of the Fibonacci-coefficient polynomials.

Mátyás, Ferenc (2007)

Annales Mathematicae et Informaticae

On the irreducibility of pure difference binomials.

R. Gilmer (1991)

Semigroup forum

On the reduction of Kronecker's modular systems whose elements are functions of two and three variables.

Harris Hancock (1900)

Journal für die reine und angewandte Mathematik

Periodicity of Recurring Sequences in Rings.

Torleiv Klove (1973)

Mathematica Scandinavica

Polynômes à valeurs entières ainsi que leurs dérivées

J.-L. Chabert (1979)

Annales scientifiques de l'Université de Clermont. Mathématiques

Polynomes a Valeurs entieres sur un anneau de Pseudovaluation.

Paul-Jean Cahen, Youssef Haouat (1988)

Manuscripta mathematica

Polynomes à valeurs entières sur un anneau non analytiquement irréductible.

Paul-Jean Cahen (1991)

Journal für die reine und angewandte Mathematik

Polynômes et dérivées à valeurs entières

Paul-Jean Cahen (1975)

Annales scientifiques de l'Université de Clermont. Mathématiques

Polynomial cycles in certain local domains

T. Pezda (1994)

Acta Arithmetica

1. Let R be a domain and f ∈ R[X] a polynomial. A k-tuple $x ₀, x ₁, . . ., x_{k - 1}$ of distinct elements of R is called a cycle of f if $f (x_{i}) = x_{i + 1}$ for i=0,1,...,k-2 and $f (x_{k - 1}) = x ₀$ . The number k is called the length of the cycle. A tuple is a cycle in R if it is a cycle for some f ∈ R[X]. It has been shown in [1] that if R is the ring of all algebraic integers in a finite extension K of the rationals, then the possible lengths of cycles of R-polynomials are bounded by the number $7^{7 \cdot 2^{N}}$ , depending only on the degree N of K. In this note we consider...

Polynomial Cycles in Finitely Generated Domains.

F. Halter-Koch, W. Narkiewicz (1995)

Monatshefte für Mathematik

Polynomial rings over Jacobson-Hilbert rings.

Carl Faith (1989)

Publicacions Matemàtiques

All rings considered are commutative with unit. A ring R is SISI (in Vámos' terminology) if every subdirectly irreducible factor ring R/I is self-injective. SISI rings include Noetherian rings, Morita rings and almost maximal valuation rings ([V1]). In [F3] we raised the question of whether a polynomial ring R[x] over a SISI ring R is again SISI. In this paper we show this is not the case.

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