Beiträge zur Algebra und Geometrie
Contributions to Algebra and Geometry
37(2), 399-414 (1996)

The Ohm Type Properties for Multiplication Ideals

Majid M. Ali

Al-Zaytoonah University
Dept. of Mathematics and Computer Science
P.O.Box 130
Amman 11733
JORDAN

Abstract: Let $R$ be a commutative ring with identity. An ideal $I$ in $R$ is called a multiplication ideal if every ideal contained in $I$ is a multiple of $I$. Ohm's properties for finitely generated ideals in Prüfer domains are investigated by Gilmer. These properties are generalized by Naoum and studied for finitely generated multiplication ideals. The purpose of this work is to generalize the results of Gilmer and Naoum to the case of multiplication ideals (not necessarily finitely generated ones).

Keywords: Multiplication ideal, Ohm condition, weak-cancellation ideal, localization

Classification (MSC91): 13A15, 13B20

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