Inertial subrings of a locally finite algebra

Yousef Alkhamees¹ ; Surjeet Singh¹

¹Department of Mathematics King Saud University PO Box 2455, Riyadh 11451 Kingdom of Saudi Arabia

Colloquium Mathematicum, Tome 92 (2002) no. 1, pp. 35-43

Résumé

I. S. Cohen proved that any commutative local noetherian ring $R$ that is $J(R)$-adic complete admits a coefficient subring. Analogous to the concept of a coefficient subring is the concept of an inertial subring of an algebra $A$ over a commutative ring $K$. In case $K$ is a Hensel ring and the module $A_{K}$ is finitely generated, under some additional conditions, as proved by Azumaya, $A$ admits an inertial subring. In this paper the question of existence of an inertial subring in a locally finite algebra is discussed.

Détail

DOI : 10.4064/cm92-1-3

Keywords: cohen proved commutative local noetherian ring adic complete admits coefficient subring analogous concept coefficient subring concept inertial subring algebra commutative ring hensel ring module finitely generated under additional conditions proved azumaya admits inertial subring paper question existence inertial subring locally finite algebra discussed