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Let $C_{F} (X)$ be the socle of C(X). It is shown that each prime ideal in $C (X) / C_{F} (X)$ is essential. For each h ∈ C(X), we prove that every prime ideal (resp. z-ideal) of C(X)/(h) is essential if and only if the set Z(h) of zeros of h contains no isolated points (resp. int Z(h) = ∅). It is proved that $d i m (C (X) / C_{F} (X)) \geq d i m C (X)$ , where dim C(X) denotes the Goldie dimension of C(X), and the inequality may be strict. We also give an algebraic characterization of compact spaces with at most a countable number of nonisolated points. For each essential...

Cycles of distance-decreasing mappings in the ring of n-adic integers

V. I. Sushchanski, E. Moćko, V. V. Nekrashevych (2006)

Colloquium Mathematicae

We give a description of possible sets of cycle lengths for distance-decreasing maps and isometries of the ring of n-adic integers.

Cycles of polynomial mappings in several variables.

T. Pezda (1994)

Manuscripta mathematica

Cycles of polynomial mappings in several variables over rings of integers in finite extensions of the rationals

T. Pezda (2003)

Acta Arithmetica

Cyclically valued rings and formal power series

Gérard Leloup (2007)

Annales mathématiques Blaise Pascal

Rings of formal power series $k [[C]]$ with exponents in a cyclically ordered group $C$ were defined in [2]. Now, there exists a “valuation” on $k [[C]]$ : for every $σ$ in $k [[C]]$ and $c$ in $C$ , we let $v (c, σ)$ be the first element of the support of $σ$ which is greater than or equal to $c$ . Structures with such a valuation can be called cyclically valued rings. Others examples of cyclically valued rings are obtained by “twisting” the multiplication in $k [[C]]$ . We prove that a cyclically valued ring is a subring of a power series ring $k [[C, θ]]$ with...

Cyclotomic equations and square properties in rings.

Fine, Benjamin (1986)

International Journal of Mathematics and Mathematical Sciences

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