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13-XX Commutative algebra

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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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