A representation theorem for Chain rings

Yousef Alkhamees, Hanan Alolayan, and Surjeet Singh. "A representation theorem for Chain rings." Colloquium Mathematicae 96.1 (2003): 103-119. <http://eudml.org/doc/284775>.

@article{YousefAlkhamees2003,
abstract = {A ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.},
author = {Yousef Alkhamees, Hanan Alolayan, Surjeet Singh},
journal = {Colloquium Mathematicae},
keywords = {chain rings; local rings; Artinian rings; principle ideal rings; coefficient subrings; separable algebras},
language = {eng},
number = {1},
pages = {103-119},
title = {A representation theorem for Chain rings},
url = {http://eudml.org/doc/284775},
volume = {96},
year = {2003},
}

TY - JOUR
AU - Yousef Alkhamees
AU - Hanan Alolayan
AU - Surjeet Singh
TI - A representation theorem for Chain rings
JO - Colloquium Mathematicae
PY - 2003
VL - 96
IS - 1
SP - 103
EP - 119
AB - A ring A is called a chain ring if it is a local, both sided artinian, principal ideal ring. Let R be a commutative chain ring. Let A be a faithful R-algebra which is a chain ring such that Ā = A/J(A) is a separable field extension of R̅ = R/J(R). It follows from a recent result by Alkhamees and Singh that A has a commutative R-subalgebra R₀ which is a chain ring such that A = R₀ + J(A) and R₀ ∩ J(A) = J(R₀) = J(R)R₀. The structure of A in terms of a skew polynomial ring over R₀ is determined.
LA - eng
KW - chain rings; local rings; Artinian rings; principle ideal rings; coefficient subrings; separable algebras
UR - http://eudml.org/doc/284775
ER -