A representation theorem for Chain rings

• Autorzy: Yousef Alkhamees , Hanan Alolayan , Surjeet Singh
• Języki publikacji: EN

Abstrakty

EN

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.

Kategorie tematyczne

• 16P20: Artinian rings and modules
• 16P10: Finite rings and finite-dimensional algebras
• 16S35: Twisted and skew group rings, crossed products

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Colloquium Mathematicum
• Rocznik: 2003
• Tom: 96
• Numer: 1
• Strony: 103-119

Daty

wydano

2003

Twórcy

autor

Yousef Alkhamees

• Department of Mathematics, King Saud University, P.O. Box 2455, Riyadh 11451, Kingdom of Saudi Arabia

autor

Hanan Alolayan

• Department of Mathematics, King Saud University, PO Box 2455, Riyadh 11451, Kingdom of Saudi Arabia

autor

Surjeet Singh

• Department of Mathematics, King Saud University, PO Box 2455, Riyadh 11451, Kingdom of Saudi Arabia

Identyfikatory

DOI

10.4064/cm96-1-10