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.
@article{bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-10,
author = {Yousef Alkhamees and Hanan Alolayan and Surjeet Singh},
title = {A representation theorem for Chain rings},
journal = {Colloquium Mathematicae},
volume = {96},
year = {2003},
pages = {103-119},
zbl = {1046.16011},
language = {en},
url = {http://dml.mathdoc.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-10}
}
Yousef Alkhamees; Hanan Alolayan; Surjeet Singh. A representation theorem for Chain rings. Colloquium Mathematicae, Tome 96 (2003) pp. 103-119. http://gdmltest.u-ga.fr/item/bwmeta1.element.bwnjournal-article-doi-10_4064-cm96-1-10/