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# Wydawnictwa / Czasopisma IMPAN / Colloquium Mathematicum / Wszystkie zeszyty

## Inertial subrings of a locally finite algebra

### Tom 92 / 2002

Colloquium Mathematicum 92 (2002), 35-43 MSC: Primary 16H05; Secondary 16L30, 13J15. DOI: 10.4064/cm92-1-3

#### Streszczenie

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.

#### Autorzy

• Yousef AlkhameesDepartment of Mathematics
King Saud University
Kingdom of Saudi Arabia
e-mail
• Surjeet SinghDepartment of Mathematics
King Saud University