On the R−automorphisms of formal power series on several indeterminates and with coefficients over the ring R

Authors

  • Soledad Ramirez Carrasco Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Av. German Amézaga s/n, Lima, Perú.
  • Anderson Cárdenas Falcón Facultad de Ciencias Matemáticas, Universidad Nacional Mayor de San Marcos, Av. German Amézaga s/n, Lima, Perú.

DOI:

https://doi.org/10.17268/sel.mat.2022.01.18

Keywords:

Automorphism, endomorphism, I-adic topology, topological ring, formal power series.

Abstract

In this paper, we show a way to characterize the R-automorphisms of formal power series on several indeterminates and with coefficients over a commutative ring with identity, R. We show this characterization, as an extension of existing result for the R-automorphisms of the formal power series in an indeterminate, given by O’Malley, M. and Wood, C. in [12].

References

Atiyah MF, Macdonald IG. Introducción al Álgebra Conmutativa. Barcelona: Reverté; 1978. 146p.

Chenciner A. Courbes Algébriques Planes. Berlin: Springer-Verlag; 2008. 160p.

Eakin P, Sathaye A. R-Endomorphisms of R[[X]] are essentially continuous. Pacific J. of Math. 1976; 66(1):83-87.

Gilmer R. On ideal-adic topologies for a commutative ring. Enseign. Math. 1972; 18(3-4):201-204.

Gilmer R. R-automorphisms of R[X]. Proc. London Math. Soc. 1968; 3(2):328-336.

Gilmer R. R-automorphisms of R[[X]]. Michigan Mathematical J. 1970; 17(1):15-21.

Gilmer R, O’Malley M. R-Endomorphisms of R[[X1; :::;Xn]]. J. of Algebra. 1977; 48(1):30-45.

Mejía CE. Automorfismos de anillos de series formales[Tesis de Maestría]. Universidad Nacional de Colombia, Facultad de Ciencias; 1985.

O’Malley M. Finite groups of R-automorphisms of R[[X]]. Michigan Mathematical J. 1973; 20(3):277-284.

O’Malley M. R-automorphisms of R[[X]]. Proc. London. Math. Soc. 1970; 3(2):60-78.

O’Malley M. Some remarks on the formal power series ring. Bulletin de la S.M.F. 1971; 99:247-258.

O’Malley M, Wood C. R-Endomorphisms of R[[X]]. J. of Algebra. 1970; 15(3):314-327.

Published

2022-07-27

How to Cite

Ramirez Carrasco, S., & Cárdenas Falcón, A. (2022). On the R−automorphisms of formal power series on several indeterminates and with coefficients over the ring R . Selecciones Matemáticas, 9(01), 210 - 226. https://doi.org/10.17268/sel.mat.2022.01.18