Abstract
Let A be a chain ring that is a faithful algebra over a commutative chain ring R, such that \(\overline{A} = A/J(A)\) is a separable, normal, algebraic field extension of \(\overline{R} = R/J(R)\) and \(\overline{A}\) is countably generated over \(\overline{R}\). It has been recently proved by Alkhamees and Singh that A has a coefficient ring R 0, and there exists a pair (θ, σ) with θ ∈ A, σ an R-automorphism of R 0 such that J (A) = θ A = Aθ, and θa = σ (a) θ, a ∈ R 0. The question of the extension of certain R-automorphisms of R 0 to R-automorphisms of A is investigated.
Article PDF
Similar content being viewed by others
Avoid common mistakes on your manuscript.
References
Alkhamees, Y., Singh, S.: Inertial subrings of a locally finite algebra. Colloq. Math. 92, 35–43 (2002)
Alkhamees, Y., Olayan, H., Singh, S.: A representation theorem for chain rings. Colloq. Math. 96, 103–119 (2003)
Ayoub, C.W.: On the group of units of certain rings. J. Number Theory 4, 383–403 (1972)
Clark, W.E., Liang, J.J.: Enumeration of finite chain rings. J. Algebra 27, 445–453 (1973)
Gilmer, R.: Multiplicative Ideal Theory, Pure and Applied Mathematics, vol. 12. Marcel Dekker, Basel, New York (1972)
McDonald, B.R.: Finite Rings with Identity, Pure and Applied Mathematics, vol. 28. Marcel Dekker, Basel, New York (1974)
Morandi, R.: Fields and Galois Theory, Graduate Texts in Mathematics, vol. 167. Springer-Verlag, Berlin, Heidelberg, New York (1996)
Author information
Authors and Affiliations
Corresponding author
Additional information
Mathematics Subject Classification (2000) Primary 16H05, 16W20, secondary 13F20, 13J15
Rights and permissions
About this article
Cite this article
Singh, S., Alkhamees, Y. Automorphisms of a chain ring. Annali di Matematica 186, 289–301 (2007). https://doi.org/10.1007/s10231-006-0006-1
Received:
Published:
Issue Date:
DOI: https://doi.org/10.1007/s10231-006-0006-1